I have seen many methods for field dressing animals and have tried quite a few of them myself. For me it really depends on the circumstance of the kill. Where I am and how I am hunting. About the only time I have a saw available is if the animal falls close to my vehicle, which is annoyingly rare. I do not carry a saw in my pack when I hunt.
JMHAT38, you can field dress any animal in N. America with only a 3"-4" blade, there is no need to carry that saw. I carry a BRKT Fox River and my usual edc folder. Keep in mind, I am talking about field dressing and reducing the animal to a size that you can get it out of the woods, not butchering. There is no need to cut any bone.
I cut around the anus (be sure and get all the connective tissue, it takes a little work) with my small edc folder before I gut. When I pull all the inards out all the nasty stuff comes out with it intact. Very clean and easy. Most people cut way too far up the rib cage. I cut the first couple of inches of the sternum, until it gets difficult, and reach in to cut the windpipe. Your taxidermist will appreciate this. If you are dragging the animal out whole ( hasn't happened for me in quite a few years) you are done. If it is a big animal or the terrain dictates smaller pieces cut into quarters at the joints. If you still need smaller pieces then start boning it out. Easy to do, again no need to cut bone. I have done this on deer, elk, bear and moose.
Last year due to the distance and terrain on my mountain goat hunt, very, very steep, I decided to clean the animal without gutting it like Evil Eye described. It worked great and very little mess.