To prepare steak, combine first 4 ingredients. Sprinkle steak evenly with sugar mixture. Place steak on grill rack coated with cooking spray; grill for 8 minutes on each side or until desired degree of doneness. Let stand 10 minutes. Cut steak diagonally across grain into thin slices.
To prepare chutney, place mango on grill rack coated with cooking spray; grill 4 minutes on each side. Cool and chop. Set aside.
Heat oil in a small saucepan over medium-high heat. Add onion; sauté 4 minutes. Add ginger; sauté 1 minute. Add vinegar, 2 tablespoons sugar, juice, 1/4 teaspoon salt, and pepper; cook 5 minutes or until liquid almost evaporates. Stir in mango; cook 1 minute. Remove from heat. Stir in watermelon, cilantro, and mint. Add mint sprigs and lime wedges, if desired.