Heat oil in a large skillet over medium-high heat. Add onion and cook until softened, about 2 minutes. Add venison and cook until crumbly, about 8 minutes.
Stir in garlic, chili powder, cumin, salt, and pepper. Cook for 2 minutes.
Deglaze the pan with lime juice and apple cider vinegar. Add water and turn heat down to medium. Simmer mixture for 8 minutes or until desired texture is reached.