To make the mint simple syrup, add the water, sugar and mint leaves to a saucepan and heat over medium heat. Whisk constantly until the sugar dissolves and the mixture comes to a boil. Let it bubble for a minute or so, then reduce the heat and let it cool completely. Remove the mint leaves before use.
Stir together the mint simple syrup, water, lime juice and lemon juice. Add the sliced limes and extra fresh mint leaves. Refrigerate for at least an hour. Stir before serving and pour over ice. Garnish with extra limes, mint and watermelon wedges.