Can your appendix be removed under regional anesthesia?

Its possible: Possible but not optimal. The best technique for appendectomy these days is minimally invasive, which means laparoscopic. That requires a general anesthetic. An open incision appendectomy could be done under spinal anesthesia or local with heavy sedation, but they certainly would not be the best choices.

Depends on surgery: If the surgeon is planing an "open" approach and the appendix has not burst, it may be appropriate to use general or regional anesthesia. However, if having a laparoscpic approach, general anesthesia will be required. Also, note that appendectomy may involved "tugging" of the appendix and surrounding tissue and the sensation may be quite difficult to completely block with regional anesthesia.

Depends on style: This surgery can be done under a high spinal, or epidural anesthesia, if it is done by the open technique. However, if the surgeon uses the usual laparoscopic technique then the regional technique will not be sufficient.