A saw is a very important tool while afield. I've used them for removing skull plates, brush, limbs and small trees to assist with processing game or moving wedged animals against small trees, and preparing a camp site and of course firewood. In an emergency situation (i.e., weather exposure and unexpected overnighters in the field - shelter and firewood) a saw will be one of your top valued tools.
As stated above, a knife is all that is needed to take the legs off at the knees and elbows and can be done in a couple seconds. A skill all big game hunter should learn.
I carry the Silky Pocketboy. I also have a Bahco Laplander and Wyoming saw which I no longer pack, Pocketboy is better. Additionally, I use a Silky Bigboy for pre-hunt wood/camp preparations. Oh, I've had the Gerber saw and the knife saw styles too, there are much better options. Stay away from the saber cut saw and any saw that make the shape of a triangle.
Good luck and buy a saw for your pack.