Add the diced watermelon and lime juice to a blender. Pulse to break up large chunks, then blend on high until smooth.
Place a fine mesh strainer over a bowl. Strain the watermelon lime juice through it, using a wooden spoon to mix and scrape the bottom of the strainer occasionally, to help it strain faster. Note:This step helps make the drink smooth and ensures there isn't any gritty texture, but you can definitely skip it if you'd like.
Add 6-8 mint leaves to a small pitcher and muddle it gently without over-mashing, about 3-4 times. Pour the watermelon drink into the pitcher and refrigerate until you're ready to serve.
Fill 12-ounce drinking glasses half full with ice. Pour the mocktail over the ice until the glasses are each about 2/3rds full. Top off each glass with seltzer. Garnish each watermelon drink with a lime slice, sprig of fresh mint, and a straw.
Notes
To make a cocktail, add 1 oz. of vodka per glass.
To boost the flavor of the drink, use watermelon flavored sparkling water instead of unflavored seltzer.
Store the watermelon lime juice separately from the seltzer in a pitcher or mason jar in the refrigerator for up to 2 days. When ready to serve, give it a shake, pour over ice, and top with seltzer.