Place the cucumbers, garlic, green onions and mint leaves in a blender or food processor and process until smooth. Add the lemon juice, water, yogurt, salt and pepper and process to combine.
Chill in the refrigerator for about 3 hours or until cold. To serve right away, pour the soup into a large mixing bowl and set that bowl into a larger bowl filled with ice and water. Stir occasionally until chilled, about 10 minutes.