Can jaw shaving/contouring be done under local anesthesia? (Photo)

This type of surgery can potentially be done without general anesthesia (that is, under IV sedation) if you can accept external scars. Typically the external approach is done from behind the ear, but they way you've drawn the line it would require an incision under the chin as well. I personally would only perform this surgery under general anesthesia due to the large blood vessels and important nerves in the field of surgery and do not want the distraction of an awake patient.