If you would like to serve alcohol-free cocktails, omit the tequila -- the drink is still delicious.
Stir together sugar and 3/4 cup water in a medium saucepan. Bring to a boil over medium-high heat, stirring until sugar is dissolved. Let cool completely. Refrigerate until ready to use, up to 1 week.
Working in batches, fill blender with watermelon cubes; blend until smooth. Pass puree in batches through a fine sieve set over a large bowl, discarding solids as you work. Refrigerate juice until ready to use, up to 1 day.
Stir together tequila, lime and watermelon juices, and sugar syrup in a large pitcher. Stir in ice and lime slices.