In a small saucepan, combine mint leaves, sugar, and rum. Simmer over low heat until the mixture bubbles slightly around the edges, then take off heat and allow to cool to room temperature.
Meanwhile, dice your watermelon and place into a blender along with the juice of 2 limes (1/3-1/2 cup) and salt.
Once cooled, strain the rum sugar mixture through a fine mesh strainer, saving the liquid. Squeeze the mint as best you can to release its natural oils. Pour the strained rum sugar into the blender.
Mix everything on high speed for about 1 minute, until everything comes together smoothly and no solid bits remain. Pour into a large sheet pan, then place in freezer.
After an hour, remove the mixture from the freezer and stir everything with a fork. Place back into freezer, and continue to scrape the mixture every half hour until it is completely frozen (it took mine about 3 hours).
Cover with plastic wrap until you’re ready to serve! Will last in freezer for 1-2 days.