Working in 2 batches, puree watermelon in a food processor. Strain puree through a sieve and strain out solids, forcing liquid out with a wooden spoon. Discard solids. Combine the watermelon puree, lime juice, mint and sugar in a 9 by 13-inch 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 1 last time and spoon into parfait glasses or bowls. Top with a mint sprig.