Heat a large skillet over medium-high heat. When hot, coat with cooking spray.
Add the carrots, celery, red and green bell pepper, onion, and garlic. Sauté the vegetables in the skillet over medium high heat for 3 minutes, or until vegetables have softened.
Add the ground venison to the skillet. Stir the meat mixture with a wooden spoon for 7 minutes, or until the meat is browned and the veggies are tender.
Add the tomato sauce, tomato paste, mustard, Worcestershire sauce, brown sugar, balsamic vinegar, salt and black pepper. Stir to combine.
After bringing the sloppy joe mixture to a boil, reduce the heat and allow to simmer for 5 minutes or until all the flavors come together.