Combine mango chunks, water and sugar in a heavy saucepan; heat until sugar is dissolved (about 10 minutes); stirring occasionally. Allow sauce to cool before pouring into blender or food processor.
Puree mango mixture in a blender or food processor; combine with lime juice and freeze for 2 hours in an ice cream freezer according to manufacturer's instructions.
Sorbet can also be made by pouring mango mixture into a baking pan and freezing for about 2 hours. Remove from freezer, run through food processor again and refreeze for an additional hour.