Does neuroticism cause people to hurt others? Is neuroticism related to harming others? Is neuroticism related to increased criminal behaviour?
And in this case, would it be useful to coach / help a neurotic person through psychotherapy?
I've edited your question somewhat; I hope I preserved its meaning.

Neuroticism relates to personal discomfort largely by definition, and probably to uncomfortable social interaction as well, though somewhat less by definition. Consider this hypothetical, mediated pathway:

Neuroticism $\rightarrow$ Anxiety $\rightarrow$ Social anxiety $\rightarrow$ Personal social discomfort $\rightarrow$ Others' discomfort

The first three of these paths are almost definitional; the last only assumes that people ordinarily feel more comfortable when interacting with others who are comfortable. Each step from neuroticism to others' discomfort changes the construct slightly, so the relationship attenuates across each step to whatever extent these mediators are all necessary, but I suspect the relationship is still reasonably strong from one end to the other. For a bit of empirical support (indirect – best I could find quickly), note that marriage satisfaction relates negatively to the neuroticism of one's partner (Fisher &amp; McNulty, 2008), though this may be less true of women with neurotic husbands (Whiteford, 2010; for other moderators, see Larson, Blick, Jackson, &amp; Holman, 2010).

The relationship between neuroticism and crime is somewhat more complex, largely because crime itself is diverse. Incarcerated populations are more neurotic (Dang &amp; Sharma, 1995; Singh, Singh, Sinha, &amp; Kumari, 1985; Eysenck &amp; Eysenck, 1971; I also found support for this via negative emotionality in my own work as a research assistant in Robert Krueger's lab at the University of Minnesota in 2005), but neuroticism may not be the best trait predictor of delinquency (self-reported; Furnham &amp; Thompson, 1991), antisocial behavior, or aggression – agreeableness seems to relate more strongly (negatively; Jones, Miller, &amp; Lynam, 2011). Neuroticism relates to these, and to substance abuse and antisocial personality disorder, but not as strongly as to agreeableness or conscientiousness (both negative correlates; Ruiz, Pincus, &amp; Schinka, 2008; see also Walters, 2014). Neuroticism doesn't predict criminal recidivism very well compared to demographic factors either (Gendreau, Little, &amp; Goggin, 1996).

As @what implied in his response to your other question, "Would most people benefit from psychotherapy?" it seems safe enough to assume that anyone could benefit from psychotherapy, criminals included. Neuroticism is often undesirable from a personal standpoint, so neurotic individuals per se might be fairly motivated therapy clients, whereas antisocial personality disorder (ASPD) is more ego-syntonic. ASPD is notoriously difficult to treat, though this reputation may be debatable. Wikipedia:


  ASPD is considered to be among the most difficult personality disorders to treat [(Gabbard &amp; Gunderson, 2000)][verification needed]. Because of their very low or absent capacity for remorse, individuals with ASPD often lack sufficient motivation and fail to see the costs associated with antisocial acts...They may only simulate remorse rather than truly commit to change: they can be seductively charming and dishonest, and may manipulate staff and fellow patients during treatment [(Oldham, Skodol, &amp; Bender, 2005)][verification needed]. Studies have shown that outpatient therapy is not likely to be successful, however the extent to which persons with ASPD are entirely unresponsive to treatment may have been exaggerated [(Salekin, 2002)].
  
  Those with ASPD may stay in treatment only as required by an external source, such as a parole. Residential programs that provide a carefully controlled environment of structure and supervision along with peer confrontation have been recommended [(Gabbard &amp; Gunderson, 2000)]. There has been some research on the treatment of ASPD that indicated positive results for therapeutic interventions [(Derefinko &amp; Widiger, 2008)]. Schema Therapy is also being investigated as a treatment for ASPD [(Bernstein, Arntz, &amp; Vos, 2007)]. A review by Charles M. Borduin features the strong influence of Multisystemic therapy (MST) that could potentially improve this imperative issue. However this treatment requires complete cooperation and participation of all family members [(Gatzke &amp; Raine, 2000)]...
  
  Therapists of individuals with ASPD may have considerable negative feelings toward clients with extensive histories of aggressive, exploitative, and abusive behaviors [(Gabbard &amp; Gunderson, 2000)]. Rather than attempt to develop a sense of conscience in these individuals, therapeutic techniques should be focused on rational and utilitarian arguments against repeating past mistakes. These approaches would focus on the tangible, material value of prosocial behavior [(Beck, Freeman, &amp; Davis, 2006); emphasis added].


An interesting interaction may occur between ASPD and neuroticism (via depression, a correlated emotional state) in predicting psychotherapeutic outcomes for substance abuse: patients with both ASPD and depression respond better than those with ASPD only (Gabbard, 2000). This further supports a mediated link between neuroticism and criminality:

Neuroticism $\rightarrow$ Substance abuse $\rightarrow$ Criminality

Neuroticism $\rightarrow$ Depression $\rightarrow$ Better outcomes for psychotherapy of substance abuse, given ASPD $\rightarrow$ Less recidivism? Worth testing at least!

References


- Beck, A. T., Freeman, A., &amp; Davis, D. D. (2006). Cognitive therapy of Personality Disorders (2nd Ed.). Guilford Press.
- Bernstein, D. P., Arntz, A., &amp; Vos, M. D. (2007). Schema focused therapy in forensic settings: Theoretical model and recommendations for best clinical practice. International Journal of Forensic Mental Health, 6(2), 169–183. Retrieved from http://www.schematherapytraining.com/storage/Bernstein.pdf.
- Dang, R., &amp; Sharma, M. (1995). Study of neuroticism and socio-demographic factors amongst female undertrials. Indian Journal of Criminology, 23(2), 65–70.
- Derefinko, K. J., &amp; Widiger, T. A. (2008). Antisocial personality disorder. In S. H. Fatemi &amp; P. J. Clayton (Eds.), The Medical Basis of Psychiatry (pp. 213–226). Totowa, NJ: Humana Press.
- Eysenck, S. B., &amp; Eysenck, H. J. (1971). A comparative study of criminals and matched controls on three dimensions of personality. British Journal of Social and Clinical Psychology, 10(4), 362–366.
- Fisher, T. D., &amp; McNulty, J. K. (2008). Neuroticism and marital satisfaction: The mediating role played by the sexual relationship. Journal of Family Psychology, 22(1), 112–122. Retrieved from http://www.recoveryonpurpose.com/upload/Neuroticism%20and%20Marital%20Satisfaction.pdf.
- Furnham, A., &amp; Thompson, J. (1991). Personality and self-reported delinquency. Personality and Individual Differences, 12(6), 585–593.
- Gatzke, L. M., &amp; Raine, A. (2000). Treatment and prevention implications of antisocial personality disorder. Current Psychiatry Reports, 2(1), 51–55.
- Gabbard, G. O. (2000). Psychotherapy of personality disorders. Journal of Psychotherapy Practice and Research, 9(1), 1–6. Retrieved from http://vuir.vu.edu.au/19368/27/00jpr001.pdf.
- Gunderson, J. G., &amp; Gabbard, G. O. (Eds.). (2008). Psychotherapy for personality disorders (Vol. 13). American Psychiatric Publishing.
- Gendreau, P., Little, T., &amp; Goggin, C. (1996). A meta-analysis of the predictors of adult offender recidivism: What works! Criminology, 34(4), 575–608.
- Jones, S. E., Miller, J. D., &amp; Lynam, D. R. (2011). Personality, antisocial behavior, and aggression: A meta-analytic review. Journal of Criminal Justice, 39(4), 329–337.
- Larson, J. H., Blick, R. W., Jackson, J. B., &amp; Holman, T. B. (2010). Partner traits that predict relationship satisfaction for neurotic individuals in premarital relationships. Journal of Sex &amp; Marital Therapy, 36(5), 430–444.
- Oldham, J. M., Skodol, A. E., &amp; Bender, D. S. (Eds.). (2007). The American Psychiatric Publishing textbook of personality disorders. American Psychiatric Publishing.
- Ruiz, M. A., Pincus, A. L., &amp; Schinka, J. A. (2008). Externalizing pathology and the five-factor model: A meta-analysis of personality traits associated with antisocial personality disorder, substance use disorder, and their co-occurrence. Journal of Personality Disorders, 22(4), 365–388.
- Salekin, R. T. (2002). Psychopathy and therapeutic pessimism: Clinical lore or clinical reality? Clinical Psychology Review, 22(1), 79–112. Retrieved from http://www.researchgate.net/publication/11564340_Psychopathy_and_therapeutic_pessimism._Clinical_lore_or_clinical_reality/file/60b7d5162d67bf28b8.pdf.
- Singh, U. P., Singh, L. B., Sinha, B., &amp; Kumari, R. (1985). Extraversion, neuroticism and criminality: A comparative study of different criminal groups. Indian Journal of Social Work, 46(2), 259–266.
- Stone, M. H. (1993). Abnormalities of personality: Within and beyond the realm of treatment. WW Norton &amp; Co.
- Walters, G. D. (2014). Drugs, crime, and their relationships: Theory, research, practice, and policy. Jones &amp; Bartlett Publishers.
- Whiteford, N. R. T. (2010). Neuroticism, marital interaction, and relationship satisfaction: An exploration of affect mediation. (Doctoral dissertation, University of Colorado at Boulder).