Mix tomato sauce, brown sugar, mustard, vinegar, and Worcestershire sauce into a small bowl; set aside. In a food processor combine the celery, bell pepper, onion, and mushrooms; pulse until finely chopped.
Heat a skillet over medium heat. Add veggies and minced garlic. Sauté for 2-3 minutes or until veggies begin to soften. Add ground turkey and cook until browned and fully cooked. Stir sauce into the skillet and cook for 5-6 minutes longer or until completely heated through. Season with salt.