1. Combine 1 1/4 cups water and sugar in a small saucepan; bring to a boil over medium-high heat. Cook for 30 seconds or until sugar dissolves, stirring frequently.
2. Remove from heat; stir in mint, lime rind, and lemon rind. Let stand 20 minutes. Strain mixture through a fine mesh sieve over a bowl; discard solids.
3. Place one-third each of sugar syrup and watermelon in blender; process until smooth. Pour puree into a large pitcher. Repeat the procedure twice with remaining sugar syrup and watermelon. Stir in lime and lemon juice. Serve over ice, or refrigerate until ready to serve. Stir before serving.