My deer usually weigh from 800 to 1400lbs. A little too big to roll over and drain. And forget cutting it's throat, wouldn't do any good anyway. I usually start skinning immediately. The animal most often is lying on his belly, so I split the hide from the base of the skull to tail. Then I start disassembling him from the top down. First I take off the head, then the front shoulders, then the hams, then cut through the spine at the point of the shoulders, removing the neck and brisket. We then cut the ribs about 10 inches down from the spine, and remove the backstrap. The ribs are last to be removed from the carcase. When we are done, the organs and intestines are still lying there on the hide, still inside their little membrane.
I learned this method from and old cowboy from Montana. That's how he did Elk as a boy. His philosophy, why mess with the organs and intestines when you don't have to. Works for me, I do all my Moose and Caribou that way. And keep the parts small enough to be handled with out hurting a bad back.