Place a large skillet over medium-high heat and brown the ground beef until no pink remains, breaking it into small crumbles with a wooden spoon.
Drain the rendered fat thoroughly and transfer the cooked beef to the slow cooker insert.
Add the diced onion, green bell pepper, minced garlic, ketchup, brown sugar, yellow mustard, Worcestershire sauce, chili powder, salt, and black pepper to the slow cooker.
Stir all ingredients until the beef is evenly coated in the sauce mixture.
Cover the slow cooker and cook on Low for 4 to 6 hours or on High for 2 to 3 hours.
Stir the mixture well before serving to redistribute the sauce.
Spoon the sloppy joe mixture onto toasted hamburger buns and serve immediately.