Add your watermelon chunks to a blender (or food processor or juicer) and blend until it becomes a smooth liquid puree.
Set your fine mesh strainer above a storage container and pour the watermelon puree through the strainer. You can stir the puree inside the strainer to make it go through faster.
The strained juice can be used immediately, or stored in the refrigerator for up to 3 days.
Watermelon Mojito
Add your fresh mint leaves to the bottom of your serving glass.
Add the sugar to the mint and use your bar spoon to stir them together. Try not to crush the mint, just stir it around and gently press the mixture against the side of the glass a few times.
Add the lime juice to the serving glass and stir it all together with your bar spoon.
Add the watermelon juice and rum to the serving glass.
Fill the glass with ice and give it a quick stir to incorporate everything together.
Top the drink with seltzer.
Add the watermelon wedge and a sprig of fresh mint as a garnish, and serve.
Notes
If you don't have a blender to make the watermelon juice, you can use a potato masher or a muddler to smash up the watermelon in a bowl. Then, put the smashed watermelon in a colander or a nut milk bag and set it over a bowl so the juice can drain out into the bowl.
Although freshly made watermelon juice is best, you can try using a store bought watermelon juice if you can find one. (Cold pressed juice will have the best flavor.)