1. In a small saucepan, bring sugar, mint, and 1/2 cup water to a boil over medium-high, stirring often, until sugar dissolves, 3 to 5 minutes. In a blender, combine fruit juices and mint syrup and puree on high to combine, 30 seconds. Pour mixture into a nonreactive shallow 2-quart baking dish and freeze until solid, about 6 hours (or up to 3 days).

2. With a fork, break granita into large chunks. Transfer to a food processor and pulse to form small crystals. Serve immediately, with mint leaves (or cover and freeze, up to 2 hours).