Combine pineapple juice, oil, soy sauce, and lime juice. Arrange tuna steaks in shallow glass pan; pour juice mixture over steaks. Cover and refrigerate for at least 1 hour. Remove tuna from marinade and place on grill 4 to 5 inches above medium hot coals; discard marinade. Grill just until fish begins to flake easily when tested with a fork, allow 10 minutes cooking per inch of thickness, turning once during cooking. Combine all ingredients in a medium bowl; stir gently, cover and refrigerate 30 minutes.
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