Tear the mint leaves in half and divide them between two glasses. Divide the sugar and lime juice between each glass (juice of 1/2 a lime per glass).
Using a muddler (or handle of a wooden spoon) crush the mint leaves with the sugar and lime juice. Add ice to each glass.
Add the rum and then pour the watermelon juice through a fine-mesh strainer into each glass (1/4 cup for each).
Top the drink off with soda water, stir, and garnish with fresh mint and/or lime slices and serve.