Cut the rind off the watermelon and discard. Cut the flesh into 2” pieces and set in a food processor or blender. Add the lime juice and honey; purée the mixture until smooth and fluid. Set a fine strainer over a bowl. Strain watermelon mixture through the sieve; use a small whisk to firmly push out a much liquid as you can. Chill watermelon mixture until needed. To serve, fill 4 tall glasses with ice cubes. Stir the watermelon mixture, and then pour into the glasses. Garnish with lime slices and mint and enjoy.