Here is skeleton of an elk any quadruped on the planet is going to have the same primary skeletal structure.
This is the Skelton of a dog the major bones are all the same. I put this up for reference to proper skeletal parts.
Here is the skeleton with muscles on. Reference this so you can see what the areas I am describing to cut look like.
Meat cuts.
Note you can do this on a gutted field dressed animal or a non gutted animal it works either way.
I lay an animal on its side and skin the animal by making a cut all the way up the hide covering the back bone from the base of the tail all the way up to the head. I then make a cut from where the cut stops at the head down across and down center of the throat. The cut all the way down to the brisket over front leg just about where it meets the brisket line all the way back and over the hind leg around to the rump and back up the middle of the hind quarter until the cut connects to where you started at the base of the tail. I then peel the skin off starting at the cut at the base of the head.
The animal is now skinned on the top half and still has skin on the bottom side that it is lying on. I lay the skin I took off, fur side down white side up and spread it out flat. I use the white, what was on the inside of the animal, side of the skin to place my meat on so they don't get dirty.
The first thing I do is take front leg off. This is simple as there is no bone connect between the shoulder and the rest of the body. Simply lift up on the front leg and remove it with a sharp knife by cutting it away from where the leg meets the rib cage on the bottom side. As you lift on the leg and cut underneath the leg will come right off. Place the leg once removed on you piece of skin being careful to not get any hair form the lower leg on the that skin.
Now I take the back straps off. This is best done by making cut across the back strap meat on the forward side of pelvis then make a deep cut along the back bone all the way up to the neck then simply fillet the back strap off the ribs. Place the back strap on your piece of skin.
Next I disarticulate the hindquarter form the pelvis. This takes some practice but once you get right the hindquarter will come off the pelvis with the sirloin attached. Place the hindquarter on your piece of skin.
Now the only thing you've got left to do is to pull the ribs off the spine. the easiest way to this is to take your bone saw and split the sternum right up the middle. After you split the sternum saw the ribs off right where they meet the backbone. Place your half ribcage on your piece of skin
Reference the skeleton picture below. the blue circles are where we removed a leg the yellow is where we've cut with a saw. The red lines are where we are going to cut through joints to make our animal manageable for packing out.
On the hind leg we cut the lower leg off at the KNEE joint NOT THE HOCK joint. This is the easiest place to separate the hindquarter from the lower leg. Once again most folks won't hit that joint on the first try but once you've done it once or twice and know where to cut a small pocket knife will slice right through that joint with ease.
On the front leg remove the shoulder from the lower leg at the elbow joint. Same as above it takes a time or two to get it and make a clean cut but once you figure out where to cut it is easy to do with a small knife on the largest animals.
Now remove the head at the atlas joint where the skull meats the spine. Or if you are leaving the head in the field don't bother.
Now before you scream at me about wasted meat on the lower legs let's talk about that. First off the lower legs or "shank meat" is usable if you want it but it is mostly tendons and ligaments. if you do want the shank meat simple cit off the bone and take it. Same goes for the neck meat.
(See the diagram below)
Elk with muscle on the bone.
Now you flip the animal over and repeat. After you're done with the other side you are left with spine and a pelvis if the gut is still attached you've probably moved the heart and lungs out of the way after cutting off the first half of the ribs. Simply remove the front loins. If the animal was not yet gutted you can make a cut in the upper flank where it attaches to the back bone and access the rear loins there. If the animal was gutted simply cut them off the bone.
I hope this was descriptive and not too confusing...