Heat olive oil in a stockpot over medium-low heat; cook and stir garlic in the hot oil until lightly browned, 1 to 2 minutes.

Heat a large skillet over medium-high heat. Cook and stir beef in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Stir ground beef into garlic. Add crushed tomatoes and tomato puree to ground beef mixture; season with salt and pepper. Cover stockpot and simmer mixture, stirring occasionally, until flavors have blended, about 2 hours.

Heat a large skillet over medium-high heat. Cook sausage links in the hot skillet until browned and no longer pink in the center, 10 to 15 minutes; drain and discard grease. Slice sausages into 1/4-inch rounds. Stir sausage, green bell pepper, and onion into the simmering tomato sauce; cook, stirring occasionally until bell pepper and onion are softened, about 1 hour.

Preheat oven to 350 degrees F (175 degrees C).

Bring a large pot of lightly salted water to a boil. Cook rigatoni in the boiling water, stirring occasionally until cooked through but firm to the bite, 10 to 11 minutes. Drain and return rigatoni to pot.

Dice about 3/4 of the mozzarella into 1/8-inch cubes. Mix cubed mozzarella with ricotta cheese in a bowl. Stir cheese mixture into cooked rigatoni until mozzarella cheese begins to melt. Pour rigatoni-cheese mixture into 2 large casserole dishes; add tomato-meat sauce. Toss well.

Slice the remaining mozzarella cheese and arrange on top of rigatoni mixtures.