In the food processor, combine the mangoes, orange zest, sugar, lime juice, and water. Process until smooth, then press through a mesh strainer into a stainless steel bowl or 9x9-inch pan. You don't want any of the pulp in the bowl, just the liquid.
Freeze until the mixture is firm 2 inches in from the sides, about 2 hours. Whip with an immersion blender or scrape with a fork until it's slushy. Repeat the freezing and whipping process 2 more times, then freeze at least 1 hour before serving.