Puree the watermelon in a blender. Strain through a fine-mesh strainer to remove any solids.

Pour 3 ounces watermelon juice, 1 ounce vodka, a squeeze of lime, a splash of St. Germain, and ice cubes into a cocktail shaker. Shake vigorously for 30 seconds. Strain into an ice-filled glass and garnish with mint and a slice of lime on the edge of the glass.