In a blender, puree watermelon. Process until smooth and there are no more chunks.
Set a large fine-mesh sieve over a pitcher. Pour watermelon puree through a sieve, pressing on solids with a rubber spatula; discard solids.
Now repeat Steps 1 & 2 with the English cucumber. Puree English cucumber in your blender and pour through a sieve into watermelon juice.
In a small bowl, stir together lime juice and honey. Add to watermelon and cucumber juices, along with vodka.
Stir the cocktail in a pitcher until well blended. Adjust sweetness with more honey if desired.
Keep the Watermelon Cucumber cocktail mixture refrigerated until ready to serve.
To serve, fill four glasses with ice and top each with cocktail mixture. Garnish with a watermelon wedge, cucumber slices and mint.