Cut grapefruit in half and thoroughly loosen all sections with a knife. Dry cut surface with a paper towel. Put sugar in a 10-inch heavy skillet and place over medium-high heat. Stir until sugar melts and darkens slightly, about 2 minutes; do not let it burn. Spread it across the pan (it will not coat evenly) and immediately add grapefruit halves, cut sides down. Move grapefruit in the pan to coat surface. Using tongs or two spoons, transfer to serving dishes, cut sides up. Sprinkle with mint and serve immediately.