Cut the watermelon into small pieces and place them in a blender.
Add mint leaves, lime juice, and simple syrup to the blender with the watermelon.
Blend on high until smooth and combined.
Pour the blended mixture through a fine mesh strainer into a pitcher to remove pulp.
Fill each serving glass halfway with ice.
Divide the strained watermelon-mint mixture evenly between glasses.
Slowly pour Prosecco into each glass, filling to the top.
Gently stir with a spoon to mix, being careful not to lose too many bubbles.
Garnish each glass with extra mint leaves and a wedge of watermelon or lime if desired.