Yep, do it all the time...

Pints...1/2 teaspoon salt and can at 10 pounds of pressure for 45 minutes...Quarts, one teaspoon salt and an hour and a half canning...
Just cube meat, pack jars to within a inch of the top, add water and take a knife and run around meat to bring air bubbles to the top, then
re-add water to within an inch of the top, add salt and seal...

I don't add other veggies for a couple of reasons:

The stock makes the best vegetable soup stock in the world...Just add veggies, 2 cans of crushed tomatoes and cook on low for a couple of hours...

A quick and easy meal...Make some rice or mashed potatoes...Warm canned venison in fry pan, add a little water and flour to thicken, add salt and pepper to taste and put on top of rice or potatoes...

BBQ...Warm canned venison, add to hot dog roll and cover with your favorite BBQ sauce, chips and a cold drink...