In a bowl, toss the cucumbers with the mint leaves. Transfer half of the mixture to a blender and puree until chunky.
In a large pitcher, combine the lemon juice, agave and matcha powder with 5 cups of ice water. With the blender on, add half of the lemon mixture to the puree and blend until very smooth. Transfer to a punch bowl. Blend the remaining cucumbers, mint and lemon mixture until very smooth and transfer to the punch bowl. Season the drink lightly with salt and serve in ice-filled glasses.