Surgery on the face

I'm not sure if i'm right, but when they perform surgury, typically the anestegeologist (spelling?) would gas you with a gas mask on your face. but what if you were having surgury on your face, how would that work out. Also would they opt to keep you awake and null a certain smalll part of your face? And how accurate would this nulling be? 2 cm? 2 inch? 2 mm? eh eh....
Really i'm just curious, i sit around and think of stupid stuff like this.