Place several of the watermelon cubes in a sieve over a large bowl. Using the back of a spoon or a muddler, press the watermelon through to extract the juice. Continue until you've used all watermelon and have approximately 1 cup watermelon juice. Add vodka and simple syrup to a bowl and stir to combine to create the cocktail mix.
Place 5-6 mint leaves in the bottom of 4 mason jars or glasses. Pour in approximately 1 tablespoon of the cocktail mix and muddle together. Add 1/2 cup cocktail mix to cups, ice, top off with 1/2 cup seltzer, and stir. Add additional mint leaves to garnish, as well as watermelon cubes, if desired.
Notes
To make simple syrup: place 1 cup water and 1 cup sugar in a small sauce pan and bring to a boil. Simmer for 3 minutes until sugar is dissolved. Set aside to cool completely before using. This will make more simple syrup than needed for this recipe; store extras in the fridge in an airtight container.