Combine sugar and watermelon juice in a small saucepan; bring to a boil. Cook, stirring constantly, until sugar dissolves.
Place watermelon cubes, lime juice, and peppermint in container of an electric blender; cover and process until smooth, stopping once to scrape down sides. Add sugar mixture; cover and process until blended. Pour mixture into a 13- x 9-inch pan; cover and freeze at least 8 hours or until firm.
Remove mixture from freezer, and scrape entire mixture with tines of a fork until fluffy. Toss mint into granita; serve immediately.
The granita may be frozen in an airtight freezer-safe container for up to 1 month.
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