Puree the watermelon in a food processor until smooth. Strain the juice into a bowl pressing on the pulp, then discard the solids.
Put the simple syrup, lime chunks, berries and mint in a pitcher and muddle until the berries are slightly crushed. Add the tequila and watermelon juice and stir to combine. Refrigerate until cold, at least 1 hour. Serve over crushed ice, garnished with mint sprigs.
Put a 1/2 cup of water in a small saucepan and bring to a boil over high heat. Whisk in the sugar and cook until the sugar is completely dissolved. Let cool.