Place beef in a slow cooker and cover with onion. Stir together 1 cup water, ketchup, Worcestershire, brown sugar, salt, paprika, and mustard in a medium bowl. Pour mixture over beef and onion.
Cover and cook on Low until meat is tender, 9 to 10 hours.
Mix remaining 1/4 cup water with flour in a small bowl to form a paste; stir into goulash. Cook on High until sauce thickens, 10 to 15 minutes.