Combine the water, sugar, and salt in a saucepan to create a simple syrup. Bring to a rapid simmer to dissolve the sugar. Once the sugar is dissolved, set aside to cool.
Peel the watermelon and cut the flesh into cubes (you should have about 2 cups.)
Use a blender to puree the watermelon until smooth.
Place a fine-mesh strainer over a bowl or pitcher and pour the watermelon puree through it to remove any seeds or pulp. Use a spoon to press the puree against the strainer and extract as much liquid as possible.
Juice 6 of the limes and add to the watermelon juice.
Slice the remaining limes into thin rounds and add to a pitcher. Add the mint and muddle to release the flavors.
Pour in the watermelon juice and club soda. Stir gently to combine.
Chill well and serve over ice. Garnish each glass with a sprig of fresh mint and a slice of watermelon, if desired.