Trim the rind from the watermelon and cut the flesh into cubes to measure 8 cups.
Add the watermelon, cold water, granulated sugar, and fresh lime juice to a blender. Blend on high until very smooth and frothy, 30–45 seconds.
Set a fine-mesh strainer over a large pitcher and pour the mixture through, pressing on the pulp to extract as much liquid as possible; discard the solids. If you prefer a pulpy texture and used seedless watermelon, you can skip straining and pour directly into the pitcher.
Refrigerate until well chilled, about 30 minutes.
Stir before serving, then pour into ice-filled glasses and serve immediately.