Place half the watermelon, half the lime juice, and half the sugar in a blender. Process until smooth, then pour into a separate bowl
Transfer mixture to a baking dish. Freeze for two or three hours, then begin the process of lightly scraping the top, frozen layer.
Repeat the occasional scraping process until the entire mixture is shaved. Store, covered in plastic wrap, until serving.
To serve, divide granita among bowls and garnish with mint leaves.
Notes
if you use a regular watermelon with black seeds, lightly blend the watermelon first, then push through a strainer to get rid of the seeds/seed particles.