Cut a sliver off the bottom of the watermelon(s) so it will sit flat. Next, cut the other end off and scoop the inside out, being careful not to pierce through the rind.
In a blender, combine the watermelon, cucumber, rum, lime juice, and agave. Blend until completely smooth. Strain the mixture through a fine mesh strainer.
Add the mint to a cocktail shaker and muddle. Stir in watermelon mixture and shake well.
Fill the watermelon or two glasses with crushed ice and pour the watermelon mix over the ice. Gently stir to combine. Garnish with a straw, cocktail umbrella, watermelon, or cucumber. Serve immediately.
For Frozen Mojito
In a blender, combine the watermelon, cucumber, rum, lime juice, and agave. Blend until completely smooth. Strain the mixture through a fine mesh strainer. Return the juice to the blender and add 1.5 to 2 cups of ice. Blend until combined and slushy. Add to the hulled out watermelon or between two glasses. Garnish and serve.
For Mocktail
For a non-alcoholic version, omit the rum and use sparkling water, Topo Chico, or lime soda. You'll need to stir the carbonated beverage into the watermelon mixer instead of mixing it in a shaker.
Notes
You can use 1 or 2 small watermelons or two glasses to serve this in.