When I am hunting, I field dress the deer where it falls. If I am going to hang it for aging, I usually hang it head up. When it's time to skin, it goes head down on a gambrel. If it needs to be skinned in camp, we hang them head up, and pull the skin off using a golf ball or rock and a vehicle with a trailer hitch or a winch. If for some reason I need to open the rib cage, I use a pair of loppers--easier and quicker than a bone saw.
That's how I do it, but I use my tractor. One time I was using my pickup and I forgot to cut the front legs off at the knee and slice them open. I started pulling and got down to the front hooves and it wouldn't come off. So I gave it a little bit too much gas and popped the head off.
I'm sure there was beer involved.