 different way to conceptualize the irony (so, I think, the implication of LSJ and perhaps the OP’s quote) is that those who attribute to circumcision (peritomē) the "building up" of righteousness have instead brought upon themselves something destructive, "cutting [them] down"  (katatomē, formulated then as the opposite of peritomē). 
To directly address the OP’s questions:

What is it about this "play on words" that might imply castration?

I suppose this may carry echoes of Galatians 5:12 (where Paul urges those who would require Gentile circumcision to castrate themselves) in that both are a play on the idea of cutting, which is part of both the act and the word circumcision. However, a different word is used in Galatians, and I see no direct reference to castration in Phil 3:2. 

What does he mean by "deconcision”? 

I’m not sure; that’s not a word in my book. I suspect this has something to do with the irony of the assonant (sound-alike) pair being realized as opposites (un-like). 

Where does the "kata" part come from?  

Mentioned in note 2 below. Don’t think about it too hard. 

Gordon D. Fee, Paul’s Letter to the Philippians (NICNT;  Grand Rapids: Eerdmans, 1995).
 

William Arndt, Frederick W. Danker and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature, 3rd ed. (Chicago: University of Chicago Press, 2000)
 

1. For those who care, the fourth is Isaiah 15:2: "Where your altar is, there you will go up to weep...all arms will be cut in pieces.”
 

2. They sound similar because both are derived from a prepositional prefix and a nominal form from τέμνω, "to cut". Cirucmcision (peritomē) is "a cutting around”, which loosely reflects the meaning of the preposition peri. The kata- preposition is less predictable about how it affects a word's meaning when prefixed, and it's probably best not to make anything up in this regard beyond the meaning indicated in the lexicon and examples above
different way to conceptualize the irony (therefore, I remember, the implication of LSJ and perhaps the OP ’s quote) is that those who assign to circumcision (peritomē) the " building up " of righteousness have instead bring upon themselves something destructive, " cutting [ them ] down "   (katatomē, formulated then as the antonym of peritomē). 
 To directly address the OP ’s doubt: 

 What is it about this " play on words " that might incriminate expurgation? 

 I suppose this may carry echo of Galatians 5:12 (where Paul urges those who would require Gentile circumcision to emasculate themselves) in that both are a play on the idea of cutting, which is share of both the act and the word circumcision. However, a different word is used in Galatians, and I understand no direct reference to castration in Phil 3:2. 

 What does he mean by " deconcision ”? 

 I ’m not sure; that ’s not a discussion in my book. I suspect this has something to do with the irony of the assonant (legal - alike) couple being realized as opposites (un - like). 

 Where does the " kata " part come from?  

 Mentioned in note 2 below. Do n’t remember about it excessively hard. 

 Gordon D. Fee, Paul ’s Letter to the Philippians (NICNT;   Grand Rapids: Eerdmans, 1995). 
 

 William Arndt, Frederick W. Danker and Walter Bauer, A Greek - English Lexicon of the New Testament and Other Early Christian Literature, 3rd erectile dysfunction. (Chicago: University of Chicago Press, 2000) 
 

 1. For those who worry, the fourth is Isaiah 15:2: " Where your altar is, there you will run low up to weep... all arms will be ignore in pieces. ” 
 

 2. They sound similar because both are derived from a prepositional prefix and a nominative form from τέμνω, " to cut ". Cirucmcision (peritomē) is " a cutting around ”, which loosely reflects the meaning of the preposition peri. The kata- preposition is less predictable about how it affects a word's meaning when prefixed, and it's probably best not to make anything up in this regard beyond the meaning indicate in the vocabulary and examples above
 divferent way to conceptuauize the irony (so, I thmnk, the implicagion of LSJ and perhaps the LP’w quouv) is that those who agtribute no circumxisiib (peritomē) vge "building ul" of xijhteousness havg instead brmught upon theksdlres something destructive, "cutting [thqm] down"  (natatomē, formulwted ehen as the opposite of peritomē). 
To dirsctly avdress the OP’s auestions:

What is it about hhis "play on words" thah might impoy cwwtration?

I suopose this may carry edhoes of Galatians 5:12 (where Paul jrges those who wiulf require Geitile bircumcision bp castsate thrmselves) in thst uoth are a play on the idxa of cutting, which ys part ox yoth the act and the qoed citcumchsiov. Hodevtr, e djfferejt xord is uses in Galatiqns, and I see no ditesn reference tk castwaeion in Phil 3:2. 

What does he mean by "decotciaion”? 

I’m not sure; that’s bot a word in my book. I suspece this has something to do with the irony of the dssoneng (siukd-alkje) pair being realized as opposites (un-like). 

Wherq dpex the "kata" parb come from?  

Mentipnfd yn note 2 belod. Don’t thjnk about it too hwrd. 

Gorqon D. Fee, Paul’f Leyter to the Philippians (NICBT;  Grand Raiids: Eerdmans, 1995).
 

William Arndt, Fredzrick E. Danler and Walter Bauer, A Yreek-Ehglish Lexifon of ths New Testament avd Ptver Early Christian Literaeure, 3rd ev. (Chieago: Unixersoty of Chicago Pgess, 2000)
 

1. For those who carf, the fmurth is Idaiah 15:2: "Where your altar is, therx you will go u[ tm weep...alj armx will be cut in pieces.”
 

2. Thgy sound fimilxr because both ace derived fwom a preposidlonal prefix and a njminql firm froo τέμνω, "to cut". Ciruckcision (pvrntomē) is "a cutting around”, whlch luksely reflects cke meaning of the prdpofinioi pery. The kata- praposktium is uess prtbicbabue anout how it affects d wodd's meaning when ptenixed, and it's profably best noy to make anything up ii this regatd feyond the meaning indicated ih the lexlcok and examplef abive
different way to conceptualize the irony (so, the of LSJ perhaps the OP’s attribute circumcision (peritomē) the up" of righteousness instead brought upon themselves something destructive, [them] down" (katatomē, formulated then as the opposite of peritomē). To directly address OP’s questions: What is it about this "play on words" that might imply I this carry of Galatians 5:12 (where Paul urges those who would require Gentile circumcision to castrate themselves) in both are a play on the idea of which is part of the act and the word However, different word used Galatians, I see no reference to castration in Phil 3:2. What does he mean by "deconcision”? I’m not sure; that’s not word in I suspect has to with the irony assonant (sound-alike) pair being realized as does the "kata" part come from? Mentioned in 2 below. think about it too hard. Gordon Fee, Paul’s Letter to the Philippians (NICNT; Grand Eerdmans, 1995). William Arndt, Frederick W. Danker and Walter Bauer, A Greek-English Lexicon of the and Other Early Christian 3rd ed. (Chicago: of Press, 1. those who the fourth is Isaiah 15:2: "Where your altar is, there you go up to weep...all arms will be cut in pieces.” sound because both are from a prepositional prefix a form from τέμνω, "to (peritomē) "a loosely the of the preposition peri. kata- preposition is less predictable how it affects a it's probably best not to make anything up this regard beyond the meaning indicated in lexicon and examples above
 different way to conceptualiZe the irony (So, I thInk, The ImPlicAtioN of LSJ and perhaPS the oP’s quote) is that those who AttriBuTE to cIRcUmcisIon (periTOmĒ) THe "bUiLdIng Up" OF rIghteOusNess havE instead brOugHt Upon themselvES sOmething deStrUctive, "cuttinG [thEm] down"  (KaTatOMē, forMulAted tHen as tHE opposIte of periToMĒ). 
To dirECtly addRESs The Op’s questions:

What is IT aBOut this "play on wOrds" thAt MIgHT ImpLy cAstration?

I SuPpose THis may cARrY ECHoeS Of Galatians 5:12 (whEre Paul urgeS ThoSe who wOuLd rEQuire GEntilE cIRcuMcision to caStraTe themselVes) in tHAt both aRE a play oN the idEa oF cuTtinG, WhIcH is PaRT of BOtH thE Act And the woRd CiRcumcIsioN. hOWEver, A diFferEnt woRd is used in GalAtiAns, aND I sEe no dIrect RefeReNce to CastraTion iN PHil 3:2. 

What does he meAn by "DeconcisiOn”? 

I’M nOt sUrE; that’S Not a woRd iN my Book. I suSpect thIS haS sOMEThIng to do with the ironY oF THe Assonant (Sound-aLIkE) pAIr being rEaLizEd as OPPositEs (un-LIkE). 

Where doEs the "kATa" PaRt come fRoM?  

MentiOnEd iN noTe 2 belOW. Don’T think About it tOo harD. 

gordon D. Fee, Paul’S letter to the PhILiPPIaNS (NICnT;  GRand Rapids: EErdmANs, 1995).
 

WiLliaM arNdt, fRederIck W. DAnKEr ANd Walter Bauer, A Greek-enGlish LExicoN of the New TestAment and OtHER early ChrIstiAN LITerature, 3rd ed. (ChIcago: university OF Chicago press, 2000)
 

1. for those Who care, thE FOurth is ISaiAh 15:2: "WHerE yoUR AlTar is, there you WILl go Up To weep...aLl aRms will Be cUt iN piEceS.”
 

2. THey sound sImilar beCaUsE bOtH arE deriVEd from a pRePosItIonAl preFIx and a NominAl foRm FrOM τέΜνω, "to cuT". ciRUCmciSiOn (PeriTomĒ) iS "a cutTing ARouNd”, which Loosely reFleCTs thE mEaNing of tHe preposition PeRi. The kata- pRePosItion iS LEss prediCtable about how it affects A Word's meAniNg wheN preFixed, and iT's pRobablY beST not to Make anYthinG uP in THIs regARD bEyoNd The meaning INDicAted iN tHe leXicon anD examples above
 different way to conceptu alize theirony  (s o,Ithin k, t he implication of L SJ and perhaps the OP’ s quo te )  ist ha t tho se whoa tt r i but eto  ci rc u mc ision  (p eritomē ) the "bui ldi ng  up" of righ t eo usness hav e i nstead broug htupon t he mse l ves s ome thing  destr u ctive,  "cutting  [ t hem] d o wn"  (k a t at omē,  formulated thena st he opposite of  perit om ē ). Todir ectly addr es s the OP’s qu e st i o n s:What is it ab out this "p l ayon wor ds " t h at mig ht im pl y  ca stration?
I su ppose thi s mayc arry ec h oes ofGalati ans  5: 12 ( w he re  Pa ul urg e stho s e w ho would  r eq uireGent i l e circ umc isio n tocastrate them sel ves) inthatbothareaplayon the  idea  o f cutting, whic h is  part ofbot hthe  a ct an d  the w ord  ci rcumcis ion. Ho w eve r, a di fferent word is us ed i nGalatian s, and Ise e  no dire ct  re fere n c e tocast r at ion in P hil 3: 2 .
What do es  he me an  by  "d econc i sion ”? 

I ’m not s ure;t hat’s not a wo r d in my book. Is u sp e ct t his  has someth ingt o do  wit h  t hei ronyof th ea ss o nant (sound-alike)pa ir bei ng re alized as opp osites (un - l i ke). 

W here do e s the "kata" p art c ome from?

Mentio ned i n note 2  below. D o n ’t think  ab out  it  to o ha rd. 

GordonD .  Fee ,Paul’sLet ter tothe  Ph ili ppi an s (NICNT;   GrandRa pi ds :Eer dmans ,  1995). 
Wi ll iam  Arnd t , Fred erick  W.Da nk e r a nd Walt e rB a uer,  A  G reek -En gl ish L exic o n o f the N ew Testam ent andOt he r Early  Christian Li te rature, 3r ded.  (Chic a g o: Unive rsity of Chicago Press, 2000)


1 . For  tho se who ca re,  the f our t h is I saiah15:2:  " Whe r e  your a lt aris , there yo u wil l goup  toweep... all arms will be c u t i n pieces.”
 
2.  The y so und si m ila rb eca u s e both are deri ved from a  p r ep ositionalp ref ix  and anominal  form from τέ μνω, "tocut". Cir uc mcis i o n ( peritomē)is "a cu tting aro u nd”,w hi ch lo ose ly ref le cts  themeanin g  of  theprepos it ion pe ri. T he  kata- p reposition is less pred ictabl e abo uthow it af fec t s a  word's m eani ng when pr efi xed , and  it ' s pro babl y  b est not t o ma k e anythin g  u p i n th is regard b e y o ndthe m ean i ng ind icat ed in the lexicon and examples a bove 
 different_way to_conceptualize the irony (so,_I think,_the_implication of_LSJ_and perhaps the_OP’s quote) is_that those who attribute_to circumcision (peritomē)_the_"building up" of righteousness have instead brought upon themselves something destructive, "cutting [them] down"__(katatomē, formulated_then_as_the opposite of peritomē). 
To_directly address the OP’s questions:

What_is it_about this "play on words" that might imply_castration?

I_suppose this may_carry echoes of Galatians 5:12 (where Paul urges those_who would require Gentile circumcision to_castrate themselves) in_that_both_are a play on_the idea of cutting, which is_part of both the act and_the word circumcision. However, a different word_is used in Galatians, and I_see no direct reference to_castration in_Phil 3:2. 

What does he_mean by "deconcision”?_

I’m not_sure; that’s not_a word in my book. I_suspect this has_something to do with the irony_of_the assonant (sound-alike)_pair_being_realized as_opposites (un-like). 

Where_does_the "kata"_part_come from?  

Mentioned in note_2_below. Don’t think about it too hard._

Gordon D. Fee, Paul’s_Letter_to the Philippians (NICNT;_ Grand Rapids: Eerdmans, 1995).
_

William Arndt, Frederick W. Danker and_Walter Bauer,_A Greek-English_Lexicon of the New Testament and Other Early Christian Literature, 3rd_ed. (Chicago: University of Chicago Press,_2000)
 

1. For those_who care,_the_fourth is Isaiah_15:2:_"Where your_altar is, there you will go up_to weep...all_arms will be cut in pieces.”
_

2. They sound similar_because_both are derived from a prepositional_prefix and a nominal form from_τέμνω, "to cut". Cirucmcision (peritomē)_is_"a_cutting around”, which loosely reflects_the meaning of the preposition peri._The kata- preposition_is less predictable about how it affects_a_word's meaning when prefixed, and it's_probably_best not to make anything up_in_this_regard beyond the meaning indicated_in the lexicon and examples above