Cut sausage into large chunks and place in a food processor. Grind sausage into crumbles. Combine ground sausage with pork, vegetables, garlic, thyme, hot sauce and a little salt and pepper. Form mixture into patties and cook 7 minutes on each side on an indoor electric grill preheated to high. To cook in a skillet, heat a nonstick skillet over medium high heat and cook burgers 6 to 7 minutes on each side. For outdoor grill, cook patties 6-inches from hot coals or over medium high gas heat 6 minutes on each side, covered.
Mix chili sauce, mayonnaise, and sweet relish in a small bowl. Serve burgers on crusty rolls with special sauce, lettuce, and tomato. Serve with red bean salad and Cajun oven fries.