Cut watermelon into 1-inch chunks.
Add watermelon to blender and blend until smooth.
Strain watermelon puree through fine-mesh strainer to remove pulp.
Fill cocktail shaker with ice.
Pour 1.5 oz vodka, 0.5 oz lime juice, 0.5 oz simple syrup, and 2 oz watermelon puree into shaker.
Shake vigorously for 15-20 seconds.
Strain into ice-filled glasses.
Top with a splash of club soda.
Garnish with mint leaves and watermelon wedges.