You may require full anesthesia because the lesion is in a tricky location for the surgeon to remove completely and ensure clear margins while you are awake. That was true for my husband; the oral surgeon's initial biopsy of a small bit of his leukoplakia -- which, like your sore, was on the underside of his mobile tongue -- was done under local anesthesia in the office, but when it came time for the ENT's excisional biopsy, which removed the whole thing along with margins, they wanted him knocked out at the hospital surgicenter.