Muddle the watermelon and mint in a cocktail shaker. Add the vodka and lime juice, and 1/2 cup of ice cubes. Place the lid on the shaker and shake vigorously for 10 seconds.
Place half a cup of ice cubes in a copper mug. Strain the mixture into the mug. Top with the ginger beer and garnish with more watermelon, mint and a lime wedge.