Whisk orange juice, lime juice, oil, vinegar, mustard, salt and pepper in a small bowl. Transfer ¼ cup dressing to another small bowl; add chicken breasts and turn to coat. Refrigerate, covered, 1 hour. Reserve remaining dressing.
Preheat grill or barbecue to medium-hot. Grill chicken until browned on one side, 3 minutes. Baste with marinade from the bowl that held the chicken. Turn chicken and grill until cooked through, 3 minutes. Transfer to a cutting board for 5 minutes. Cut into thick slices.
Combine remaining dressing, mango, tomato, cucumber and onion in a large bowl. Add the grilled chicken. Serve over salad greens.