In a small saucepan, combine the sugar and water. Cook until the sugar is melted and the syrup is clear. Turn off the heat and add the mint leaves to the syrup.
Cover the pot and let the leaves steep for 10 minutes. Then, strain the mint from the simple syrup and discard the leaves.
While the mint syrup is steeping, cut up watermelon into cubes and place in blender. Process the watermelon until it's smooth, about 30 secs. Strain the watermelon juice through a sieve to remove any pulp or seeds.
To a collins glass add 4-6 mint leaves, 1 slice of lime, and about 2 teaspoons of mint simple syrup and muddle. (Bruising the mint makes the mint leaves sweet. If you tear the mint leaves, they will taste bitter.)
Add ice to the glass, pour in 2 ounces of rum, and stir.
Pour 1/4 of the watermelon juice into the glass, filling it about 3/4 full. Then top with 2 ounces of club soda. (At this point, you can add more simple syrup if you like.)
Add a few more mint leaves and lime slices to the glass. Then garnish with a watermelon slice and enjoy!
Notes
You can make the mint simple syrup and watermelon juice ahead of time and store them in air-tight containers in the fridge until you're ready to mix.