Place a large skillet over medium-high heat. Add the ground pork sausage and diced green bell pepper. Cook for 5–6 minutes, breaking the meat into small crumbles with a spoon, until the sausage is completely browned and no pink remains.
Remove the skillet from the heat. Carefully drain the excess grease from the sausage and pepper mixture using a colander or paper towels.
Transfer the drained sausage and peppers into the insert of a 4-to-6-quart slow cooker.
Add the cubed processed cheese, shredded sharp cheddar cheese, and the entire undrained can of diced tomatoes with green chilies to the pot.
Cover the slow cooker with its lid and set the temperature to LOW. Cook for 2 hours, stirring thoroughly every 30 minutes to help the cheeses melt evenly and combine with the sausage juices.
Once completely smooth and melted, turn the slow cooker to the WARM setting for serving. Serve alongside sturdy tortilla chips or sliced vegetables.