I'm hoping to do a video on this pretty soon. I can do one in 5 minutes without much trouble. I start by slicing along the brisket from the front of the rib cage to the diaphragm. Then I cut about 6" down from the end of the rib cage just to get my cut started. After that, I use a saw to cut open the rib cage. Once that's open, I hold the hide by making an upside down Y with my fingers. I lay the knife in the middle of my fingers and cut down to the pelvis. I then grab both rear legs and pull them together and push forward to gain access to the butthole. A quick run around the ballon knot with the knife, then I go back to the saw and cut through the pelvis. After that, cut the diaphragm and windpipe, then pull. It'll all come out nice and clean. (I use my left hand during all this to hold the stomach in place after I open it from ribcage to pelvis.) On a buck I'm mounting, I don't cut the hide north of the diaphragm and I cut the penis/balls out in one package. When it's warm, I cut a does teets off if she has milk.
I've seen a lot of guys talk shit about my technique, only to watch them do a 15 minute butcher job while attempting to "show me how it's done". I gut 4-5 deer a year and I've developed a pretty effective technique as a result. Not saying it's the best or the only way, but I'll race for speed and cleanliness of the finished product any day, with any one!
I had Tracie's done last week in 4:15 and when we dropped it off the processor said: "Sure wish more people would get 'em this clean before dropping them off..." I take pride in doing a good gut job. I see it as one more vital step in the entire process. I also hang all my deer and wash them out before doing anything with them. Since I have all my deer processed, I don't believe in making them work any harder than they already have to.
I'm sure we'll have a deer on the ground for muzzleloader, so I'll try to do a video then.