Never cut a neck. I don't really think it is inhumane though.
My My brother in law is a crack shot. He is only 17, but he like to show off and head shoot deer. Well 2 years ago is was hunting the big box with my father in law and a good 8 point walked out and he aimed for the eyeball and the deer dropped.
My father in law would rather clean 2 so he climbed down to drag the deer off the lane so he could hunt some more. When he walked up there wasn't any blood and one antler was missing. He reached down to and grabbed the other antler to look at the other side and the deer rolled its eyes. Sat down quickly on the front shoulder and cut the throat.
My brother in law had hit the base of the antler and knocked the deer out cold. They agrued the rest of the day about who should tag it.
That is about the only way I would advocate cutting a throat. if you know you don't have a shot to finish him with your rifle on the ground but you are going to be in trouble if he gets up.