1) Working in two batches, puree the watermelon in a food processor. Strain the puree through a sieve and strain out the solids, forcing the liquid out with a wooden spoon. Discard the solids.
2) Combine the watermelon puree, lime juice, mint and sugar in a 23 by 22-cm metal pan. Place mixture in the freezer, scraping thoroughly with a fork every 20 to 30 minutes for about 2 1/2 hours, or until the granita resembles coarse crystals. Scrape one last time and spoon into parfait glasses or bowls.