Make the Granita: Combine sugar and 1/4 cup water in a small saucepan, bring to a boil, and immediately remove from heat. Stir the grapefruit juice and Campari together in a large bowl. Add the sugar mixture to the juice mixture, stir to combine, and let cool slightly. Transfer the mixture to an 8- by 12-inch baking pan (the liquid will reach about 3/4 inch up the sides of the pan), cover the pan with plastic wrap, and freeze until firm -- about 8 hours.
Serve the Granita: Working quickly, scrape the surface of the frozen granita with a fork to make large ice crystals.
Spoon the granita into individual dishes and serve immediately.
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