Combine the watermelon, cucumber, lime juice, salt, and mint in a blender and blend until smooth.
Strain the mixture through a fine-mesh sieve, pressing to release all the liquid.
Into a tall glass filled with ice, pour ½ cup of the watermelon mixture and top with ½ cup or more of the sparkling water. Stir in agave to taste, if using.
Slip slowly until you've recovered. Have another glass if you need it. Store any remaining cooler covered in the refrigerator for up to 1 day. Stir well before drinking.