Cook the pork sausage in a large skillet over medium heat, breaking it into crumbles, until fully browned with no pink remaining. Drain excess fat if needed.
Transfer the cooked sausage to a slow cooker. Add the processed cheese, cream cheese, and undrained diced tomatoes with green chiles.
Cover and cook on Low for 1 to 2 hours, stirring occasionally, until the cheeses melt and the dip is hot and smooth.
Switch the slow cooker to Warm and serve the dip with sturdy crackers, chips, bread, or vegetables.