1Mix vinegar and water in small bowl. Stir in dressing mix. Stir in oil. Divide dressing mixture in half.
2Place beef in shallow glass or plastic dish or heavy-duty resealable plastic food-storage bag. Pour half of the dressing mixture over beef; turn beef to coat. Cover dish or seal bag and refrigerate at least 2 hours. Cover and refrigerate remaining dressing.
3Heat coals or gas grill for direct heat. Remove beef from marinade; reserve marinade. Cover and grill beef 4 to 5 inches from medium heat 15 to 20 minutes, turning and brushing with marinade occasionally, until desired doneness. Discard any remaining marinade. Cut beef into 3x 1/4-inch slices.
4Divide salad greens, arugula, tomatoes and mushrooms among 4 plates. Top with beef; drizzle with remaining dressing. Sprinkle with cheese and croutons.