Cut the watermelon into cubes and juice or blend them until you have 2 1/4 cups of juice. Strain through a fine-mesh sieve to remove pulp and seeds, pressing gently to extract all the liquid. Set the strained juice aside to chill while you prepare the remaining components.
In a pitcher, combine the cold sweet tea and fresh watermelon juice from Step 1. Add the fresh lime juice and stir well to blend all components evenly. Taste the mixture and adjust the flavor balance—add a touch more lime juice if you want extra brightness, or more sweet tea if you prefer it less sweet. I like to add the lime juice gradually because watermelon's sweetness can mask its tartness until everything is well combined.
Fill serving jars with ice and pour the watermelon iced tea mixture from Step 2 over it. Gently tear 1-2 fresh mint leaves per glass and drop them onto the surface of each drink. The mint will float on top and release its aroma as you sip, adding a fresh herbal note that complements the watermelon and lime beautifully.