Crumble the beef mince into a large pot or Dutch oven over medium-high heat. Cook, stirring frequently until evenly browned. Drain off grease. Add the onion and celery and cook until the onion is tender, about 3 minutes.
Reduce heat to medium and pour in the chilli sauce. Stir in the vinegar and sugar. Add mustard if using. Simmer until the mixture is your desired thickness. Serve on hamburger buns.