Retract an already submitted recommendation letter (written for an undergrad student)
I think you should do nothing.

(Nothing with respect to the letter, that is.  You may of course want to consider intervening with the student as you would with any other student whose performance suddenly drops off.  As Azor Ahai says, he may be experiencing some sort of academic or non-academic problem.)


  By putting my name on the letter I effectively vouched for him and his ability to perform at a certain level. To me, it's as if I made a promise to the other university, but now I see that I misled them (albeit unintentionally).


I don't see it that way.  You couldn't possibly make promises about his future performance, and the receiving university will not have interpreted it that way.    They are well aware that "past performance is no guarantee of future results". Provided you made an honest assessment based on what you knew at the time, your letter was in no way misleading, and you have no obligation to correct it.

Proactively sending a followup unrecommendation would come across as somewhat vindictive, and I think it's sort of an ethical gray area.  The student consented to having you send a letter, sharing his academic progress, at a particular time; I think it's a little questionable whether that consent extends to having you send additional letters.  (However, if the other university should contact you to ask about him, I do think it would be appropriate to give them an update on his more recent work - but to me that feels different.)

That said, I don't think the student is really likely to profit from this anyway:


Your initial letter, saying "I've known him for half a semester and so far he's doing fine in this one class", can't really have done much good for his application in the first place.  If the other university is "much stronger", having such a letter, in place of a very positive letter from someone that knew him well, may have sunk his application from the outset.
If he does receive an offer of admission, it will almost certainly be contingent on continued satisfactory academic progress.  The other university will review his final transcripts before he actually starts in the program.  If he receives a poor grade in your class, they may very well revoke his admission.  Indeed, discussing this possibility with the student may encourage him to shape up.