In a blender puree watermelon pieces , then strain through a fine mesh sieve to extract as much liquid as you can. (We need about 3 oz watermelon juice for a single cocktail).
In a large glass combine mint, simple syrup and lime juice. With the back of a wooden spoon (or you can use a wooden rolling pin) muddle, but don't break mint leaves. Add ice. Pour in watermelon juice, rum and soda water. Stir to combine.
Serve mojitos garnished with mint springs, lime wedges and a slice of watermelon.