Finely chop 1 mango and 1 cucumber and set aside. Coarsely chop remaining mango and cucumber and puree with 1/4 cup water in a blender until almost smooth. Transfer to a bowl and stir in finely chopped mango and cucumber, onion, lime juice, and 2 cups cold water. Place bowl in a larger bowl of ice and cold water and stir until cool.
Just before serving, stir in cilantro and 1 1/4 teaspoons salt.