This may be a bit long-winded, but if you want to save lots of work and time and processing costs, try this technique vs. the traditional field dressing/hauling out the entire carcass, especially appropriate if you don't care about saving a cape for a mount or tanning for leather ––- important secret revealed!!!
Assuming the expired animal is lying on its side on the ground (if not, deal with it accordingly, as follows...), start with cutting the hide from nape of neck to root of tail along the dorsal surface, i.e., backbone. Then, skin shoulders, rib cage, hams, hocks, etc. on the "up" side, exposing all the muscle groups/meat on the upside of the animal, laying the hide on the ground/snow/mud/whatever to create a clean "apron" on which to place the boned out meat.
Carefully detach the backstraps from the spine, removing them (one on each side of the spine) as long, thick "ropes" of steaks. Keeping the backstraps intact as one recognizable piece will be helpful later in identifying these premium cuts. Then, using the membranes separating the various large muscles as guidelines, detach the big muscle groups from front shoulders and hams ––- these can be dealt with as roasts or ground or chunked for stew or whatever , depending on the age, tenderness, etc. of the animal in question. As you work, you can temporarily place the boned muscles on the inside of the skin "apron", keeping the meat clean until you've placed it in game bags, or etc.
Before you flip the carcass over to work on the reverse side, be sure to get the tenderloins, the best cuts on any mammal, which lie on the "inside " of the spine, and which are very loosely attached. This is delicate work, best done with a small, short knife blade, and careful tugging. The forward end of the torpedo-shaped tenderloins are attached by tendons about two ribs forward of the rearmost rib, and the aft end a little bit behind the last rib. Use one hand to depress the stomach lining away from from your work (do NOT puncture stomach lining!) and carefully, cautiously tug and cut out the tenderloins, which, unlike other cuts, do not need aging and can be consumed the very day of the kill, as a reward for your success!
Flip the animal over, using its by now rigor-mortised legs as levers, and repeat on opposite side. This technique does not involve eviscerating the animal, create a big, sloppy, fly and yellow-jacket infested bloody gutpile to work in, and salvages every bit of useable meat on any large ungulate save the scanty bit of meat on the ribs. Its neat, clean, especially sanitary, and lets the meat cool quickly. It does NOT preserve evidence of sex, so save whatever bits your state game laws require. This technique also essentially ruins the hide for taxidermy, but so what. A reminder ––- you may want to pull the "tusks" from elk or similar trophy parts from the carcass before abandoning it.