In a small saucepan, bring the water to a simmer with the sugar and stir over moderate heat until the sugar is dissolved, about 1 minute; let the sugar syrup cool.
In a blender, puree the watermelon until smooth. Set a fine-mesh strainer over a bowl and strain the watermelon juice, pressing gently on the solids to extract as much juice as possible. Discard the pulp and save the juice.
In a large pitcher, combine the sugar syrup with the lime juice, blueberries and mint leaves. Using a wooden spoon, lightly muddle the blueberries and the mint. Add the watermelon juice and tequila. Refrigerate until chilled, about 2 hours.
Pour the cocktail into tall ice-filled glasses. Garnish with mint sprigs and watermelon wedges and serve.