To prepare sauce, combine the first 6 ingredients; cover and chill.
To prepare beef, soak wood chips in water 1 hour.
Remove grill rack; set aside. Prepare grill for indirect grilling, heating one side to medium-high and leaving one side with no heat.
Place half of wood chips on hot coals. Place a disposable aluminum foil pan on unheated side of grill. Pour 2 cups water in pan. Coat grill rack with cooking spray; place on grill.
Sprinkle beef evenly with pepper and salt. Place beef on grill rack over foil pan on unheated side. Close lid; cook 55 minutes or until a thermometer registers 135° or until desired degree of doneness. Add additional wood chips halfway through cooking time. Remove beef from grill. Cover lightly with foil; let stand 15 minutes. Cut beef across grain into thin slices. Serve with sauce.