Blend: Scoop the fruit out of the watermelon. In a blender or food processor, puree watermelon until it reaches a thin, even consistency. You should have about 6 cups of watermelon juice. If you have seeds in your watermelon, strain them out with a mesh colander. Stir in lime juice and sugar.
Freeze: Pour into a large baking dish and freeze for about 2 hours. Remove and scrape at frozen sides and top. Place back in freezer. Repeat this process of freezing and scraping, every few hours, until mixture is completely frozen and scraped.
Store granitas in the freezer in an airtight container.
Make it a grown up granita! Add ½ cup of vodka when you add the lime and sugar. This version will be a bit more slushy, as the vodka will not freeze solid.