Dissolve the sugar in the lemon juice. Pour out 1/4 cup vodka and add the lemon mixture and the mint sprigs to the bottle. Cap, shake, and let sit from 1 hour to overnight for the flavors to develop.
Cut a plug from the watermelon about 3-inches deep and as big around as the top of the bottle. Upend the bottle into the hole and let it sit for a couple of hours or until most of the vodka lemonade has been absorbed into the watermelon. Re-plug the watermelon and refrigerate it for a few hours. Slice and serve.