Combine hoisin sauce and next 7 ingredients (hoisin through garlic) in a small bowl; stir with a whisk.
Sprinkle tuna steaks with salt and pepper. Add wood chips to grill. Place tuna steaks on grill rack coated with cooking spray; cook 5 minutes. Turn and baste tuna with hoisin mixture; cook 5 minutes. Turn and baste tuna with hoisin mixture; cook 2 minutes or until tuna flakes easily when tested with a fork.