Ive only been put in this situation once, but it was in season. I walked up on what I thought was a dead deer but turned out to be a young b-buck that had its front shoulder shot to hell with bones and meat sticking out everywhere. He was too weak to move and obviously in alot of pain. At one point I snuck around him in a creek bed and popped up over the bank 5ft from him. He had enough energy to raise his hind legs to try and stand and then just fell and stared at me staring at him.
I felt so bad for this animal I turned around and made the mile walk back to my house and returned with my 870. I stayed just out of his view to keep from worrying it more and put a slug through his head to make it quik.
I'd have to say that if I ever saw a deer in that situation again, in season or not I would definately put the thing out of its misery.