Combine sugar and water in a small saucepan. Bring to a boil and simmer until the sugar has completely dissolved. Remove from the heat and cool completely.
In a blender or food processor, purée all the watermelon flesh and pour it back into the watermelon punch bowl.
In a small mixing bowl, muddle the mint leaves, simple syrup, lime juice and rum. Pour into the punch bowl and stir to combine it with the watermelon purée.
Serve over ice and garnish with mint.