Might i have my mole removed under general anesthetic?

It depends: Most moles are removed under local anesthesia and rarely with twilight or mac anesthesia. Depending on the location and size of your mole, general anesthesia may be indicated. You should consult with your surgeon and anesthesiologist to determine the suitabilty of general anesthesia for your procedure.

Yes: Yes, but it would generally be better done with local anesthesia unless the surgeon expects more extensive involvement.