To a blender, add the watermelon, cucumber, and mint leaves. Puree until smooth. Strain into a measuring cup or pitcher through a fine mesh sieve.
Add a few ice cubes and a slice of watermelon to two glasses. In a shaker, combine the watermelon puree, St. Germaine, and lime juice. Add ice and shake until cold. Strain into two glasses. Top with prosecco and garnish with a sprig of mint.