Which type of doctor deals with puncture and/or acupuncture?

Lots of kinds: "medical acupuncturists" are do and md who have additional training in acupuncture. Acupuncturists may also be trained via tradional chinese medicine. Acupuncturists may be psychiatrists, ob/ gyn, orthopedics, anesthesia, neurosurgery, family practice, er, sports medicine, flight surgery etc.

?: Doctors who perform acupuncture are generally doctors of chinese medicine or dom (doctors of oriental medicine). A doctor who deal with puncture wounds is usually your general practitioner or the er doctor. I think you mean a dom!