Heat olive oil in a skillet over medium heat. Stir in onion and cook until softened, about 3 minutes. Stir in garlic and cook until softened, about 2 more minutes. Remove the skillet from heat.

Place venison roast into a slow cooker and sprinkle with onion mixture. Stir together ketchup, water, Worcestershire sauce, soy sauce, chile-garlic sauce, pepper, salt, and liquid smoke in a small bowl until well combined; pour over venison.

Cover and cook on Low until tender and no longer pink, 4 to 5 hours.