Cut the grapefruit in half and thoroughly loosen all sections with a knife. Dry the cut surface with a paper towel. Put the sugar in a 10-inch heavy skillet and place over medium-high heat. Stir until the 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 the grapefruit halves, cut sides down. Move the grapefruit in the pan to coat the surface. Using tongs or two spoons, transfer to serving dishes, cut sides up. Sprinkle with mint and serve immediately.