In a blender, combine the cubed watermelon, grated ginger, lime juice, and honey or agave syrup. Blend until smooth.
Strain the mixture through a fine mesh sieve into a large pitcher to remove any pulp, pressing down with a spatula to extract as much juice as possible.
Fill glasses with ice cubes and pour the watermelon ginger juice over the ice, filling each glass about two-thirds full.
Top each glass with sparkling water, stirring gently to combine.
Garnish with fresh mint leaves if desired, and serve immediately.