place the watermelon, cucumber, mint leaves, and salt in a blender pitcher. If you’re using a food processor you may need to work in batches.
Start on slow speed until roughly chopped, then increase speed and blend until smooth (1-2 minute) – if your equipment tends to get hot, work in batches to prevent heating the ingredients.
Strain the puree through a fine mesh strainer. This step is optional but yields a more attractive, stable final product.
At this point, the juice may be enjoyed on its own, or proceed to making a cocktail.
For each cocktail, put 1.5-2 ounces of rum into a mixing glass filled with ice. Add 10-12 ounces of juice and 2-4 dashes of bitters. If you have a shaker, shake well. Otherwise, stir. Fill a serving glass with crushed ice (cubes are fine too) and strain the cocktail into the glass. Garnish with a sprig of mint.