Can I sue the doctor that circumcised my son if he did not perform it correctly?

Yes, you may have a cause of action if malpractice was committed. Malpractice is medical care which does not rise to the level of current generally accepted standards of care--i.e. the doctor did something wrong. (Note: it's not enough that there was a bad outcome, since sometimes the best doctor does everything right and the patient still suffers--medicine is not an exact science; there must be some carelessness, mistake, etc. on the part of the doctor.)

If this doctor performed the procedue in a way that did not meet accepted standards, he may have committed malpractice and you may have a cause of action. You should consult with a malpractice attorney to evaluate the strength and value of this case.