Cook beef mince in a large frypan over medium heat until no longer pink. Stir frequently, and break into pieces. Drain off grease.
Add onion, celery and green capsicum to the frypan, and season with salt and pepper. Cook, stirring until onion is soft, about 5 minutes. Stir in tomato sauce, vinegar, sugar, Worcestershire sauce, and tomato puree. Cover, reduce heat to low, and simmer for 20 minutes. Spoon onto buns, and serve.