Combine lime juice and next 5 ingredients in a large heavy-duty, zip-top plastic bag; seal bag, and marinate in refrigerator 30 minutes.
Remove turkey from bag, reserving marinade. Place marinade in a saucepan. Bring to a boil; remove from heat. Coat grill rack with cooking spray; place turkey on rack over medium-hot coals (350° to 400°). Grill, covered, 10 minutes on each side or until turkey is done, turning and basting frequently with reserved marinade. Cut turkey diagonally across grain into thin (1/4-inch-thick) slices. Serve turkey with Mango-Papaya Salsa.