Place water and sugar in a medium-size saucepan and bring to a simmer over medium heat. Stir until sugar dissolves, about 3 minutes. Remove from heat and pour into a large bowl and allow to cool. Stir in lime juice.
Place mango and mango juice into a blender and puree. Stir into sugar syrup. Pour into a shallow metal pan and freeze for 3 to 4 hours. Stir mixture every hour, spooning ice crystals from side of pan into middle.
When mixture is frozen, place in food processor and pulse for about 5 seconds to form a snowlike mixture.
To serve, spoon into dessert dishes and garnish with lime slices if desired.