Place chopped mango in the bowl of a food processor fitted with the metal blade, and process until smooth. Transfer to a medium bowl. Add the water, lime juice, and sugar, and stir to dissolve.
Pour mixture into a 9-by-5-inch deep-sided metal pan, and place in the freezer until nearly set, about 3 hours, whisking mixture every hour. Remove from freezer, and scrape surface with the tines of a fork until it is the texture of shaved ice. Return to freezer until ready to serve. Granita can be stored in an airtight container in the freezer up to 2 weeks.