Do I need to bag my brush cuttings

Not if you're taking it to the dump but if you're putting it in your container at home then yes

Yes, per county and City code, all trash, including yard waste, must be bagged and tied prior to placing in your trash container. You do not need to bag yard waste if bringing to the Recycling-Solid Waste Collection Center. You can also schedule a free curbside bulk collection by calling 480-782-3510. Trimmings to not need to be bagged for bulk pick up. Loose items such as leaves and small trimmings do need to be bagged for easy pick up. Thank you.