Place four martini glasses in the freezer to chill for at least 30 minutes.
Place a food mill fitted with the largest disk over a bowl. Add the watermelon and pass it throw the mill; you should end up with about 2 cups of watermelon juice. Pour into a pitcher and discard the seeds and pulp. Stir in the vodka, Cointreau, and lime juice.
Fill a cocktail shaker half full with ice, pour in the cocktail mixture, and shake for a full 30 seconds. Pour into the chilled martini glasses and garnish each glass with a sprig of mint. Serve ice cold.
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