Add the watermelon to a blender and blend until completely pureed. Strain the mixture through a fine mesh sieve over a measuring cup and use a spoon to press every last bit of liquid out of the watermelon pulp.
Add the watermelon juice and sugar to a small saucepan over medium heat. Stir constantly until the sugar dissolves and once the liquid comes to a boil, turn off the heat. Pour the juice into a 9×13-inch baking dish and whisk in the rum. Freeze for 4 hours then use a fork and scrape the mixture into small icy bites. Freeze again and repeat the scraping one or two more times withint the next two hours or so.
When ready to serve, open the can of cold coconut milk and discard (read: use it for something else, don’t pitch it!) all of the liquid. Scoop the cream into the bowl of an electric mixer and beat on high speed with a whisk attachment until peaks form, about 2 minutes. If desired, you can sweeten your coconut whipped cream with a little sugar. Serve the granitas by layering a spoonful of the whipped cream, the granitas and more whipped cream. Add a spring of mint if you wish!
Note: you can obviously use regular whipped cream if you wish and a different booze too!