1. Remove rind from watermelon, cut into 2-inch chunks, and remove seeds. Arrange in a single layer on a parchment-lined baking sheet, or in a resealable plastic bag; place in freezer until frozen, about 1 1/2 hours. (Transfer to airtight freezer bags if not using immediately.)

2. Place frozen chunks in a food processor; process until smooth. Add sugar, lime juice, and Campari; process until fully incorporated, about 5 minutes, scraping down as necessary. Freeze in an airtight container, at least 2 hours, until firm. Stir if juice starts to separate from ice.