Over the years, the way I've cooked venison has evolved. The native big game species where I grew up (Black Hills of SD) was white tail deer. With in easy driving distance mule deer and pronghorns were also readily available. We processed them similar to the way cattle are butchered.... in terms of "cuts"
More often than not, some if not most of the mule deer (and often the white tail deer) "cuts" were disappointing... Especially any steaks not cut from the back-straps. Even when "swissed", they could be dry and gamey.
Now that I live in an area where I can hunt elk and mule deer, and where my mom is no longer the cook, I do things differently: Elk is still processed similar to beef, and to an extent, cooked in a similar fashion.... It is usually just slightly more of a workout for the teeth and jaw, but not bad. With mule deer on the other hand, only the back-straps are cut into steaks (usually thick enough to be butterflied before grilling) and the tenderloins are are kept whole (and again usually grilled).
Every thing else becomes roasts, jerky, salami, stew meat and/ or burger. Burger is usually ~ 80/20 coarse grind with fatback and bacon trimmings. The burger is typically used for chili, taco meat and spaghetti, but usually never "hamburgers".
I typically have the salami, and burger done by a local processor that specializes in these products from wild game.
A few (or most, depending on the year) of the roasts are cut up for jerky; marinated in a mixture of salt, brown sugar, granulated garlic, red chile powder, cayenne, Jack Daniels, and apple cider... and smoked.
Any remaining roasts are marinated in buttermilk for 24 hrs. before cooking. The enzymes and the "saltiness" of the buttermilk break down the connective tissues, start to pre-digest the meat ( I know that sounds kind of gross), and neutralize any rankness or gamey flavor... Often the tenderloins, and steaks from the back-straps get this same buttermilk treatment. Before cooking just wipe (not rinse) them off and season as you see fit. Salt, pepper, and Granulated garlic are a good starting place.
The roasts are seasoned, pan seared, and then go into an enameled dutch oven with onions, carrots, celery, and (as ppine suggested) a sweet acidic braising liquid, or even a dark beer.
Then cover and braise in the oven at 275-300 until tender.
You can also use this same procedure and instead "pressure steam" them in a pressure cooker by using a support trivet to keep the meat elevated out of the cooking liquid. This is the quickest method, and usually renders the most tender results.
If you do happen to have steaks cut from the "quarters" I suggest cutting them into thin-ish strips, then 24 hrs. in the buttermilk marinate , and use them to make stroganoff (my all time favorite and traditionally made in Russia with "venison"), or fajitas.