Combine sugar and 1/4 cup water in a small saucepan and cook over low heat until the sugar melts, 3 to 4 minutes. Remove from the heat and set aside to cool, about 15 minutes.

Combine mangoes, the simple syrup (water and sugar mixture), lime juice, and 1 cup of water in the bowl of an electric blender; blend until smooth, then strain through a fine sieve into a pitcher. Add remaining water and fresh mint, stir, and chill for at least 2 hours before serving.