Grapefruit sections and fresh mint top Italian ice, or granita.
In a small stockpot, bring juice, sugar, and 3 cups water to a boil; stir, and remove from heat. Add grapefruit; let stand 5 minutes. Using a slotted spoon, remove grapefruit; cover, and refrigerate. Add Campari to liquid, and pour into a metal bowl. Set over a bowl of ice water to cool.
Transfer liquid to a 9-by-13-inch glass baking dish; cover with plastic. Freeze until mixture begins to set, about 30 minutes. Scrape icy particles from sides, stir with a fork, and return to freezer. Repeat scraping and stirring every 30 minutes until mixture is frozen with a grainy texture, 2 to 2 1/2 hours.
Serve granita with grapefruit and mint.