In a blender, combine the chopped cucumbers and lime juice. Blend until smooth.
Strain the mixture through a fine mesh sieve into a large pitcher to remove the pulp, pressing down with a spoon to extract as much liquid as possible.
Add the coconut water, honey or agave syrup, and sea salt to the cucumber-lime juice in the pitcher. Stir well until the sweetener is fully dissolved.
Taste the agua fresca and adjust sweetness if necessary by adding more honey or agave syrup.
Chill the mixture in the refrigerator for at least 30 minutes before serving.
Serve over ice cubes and garnish with fresh mint leaves if desired.