In a blender, puree the watermelon until smooth. Strain through a fine mesh sieve into a bowl or pitcher to remove pulp.
Place mint leaves in a glass and gently muddle them using a muddler or the back of a spoon to release flavor.
Add lime juice and agave syrup (or honey) to the glass. Stir to combine.
Fill the glass halfway with ice, pour in the strained watermelon juice, and top with club soda.
Stir gently and garnish with a wedge of watermelon and a sprig of mint before serving.