Yes, cutting a tree's roots can cause it to fall, particularly if major support roots are severed. In extreme cases, trimming roots can affect the tree's structure and stability. Many crucial roots are located just below the soil's surface. If you make severe cuts to roots more than 2 inches in diameter, you risk impacting the tree's water flow and its ability to withstand severe winds or storms. Even cutting roots less than half an inch in diameter under or outside the tree's canopy can cut off its water supply, causing it to decline, die, and eventually topple.

It is possible to cut down a tree on your property yourself, but it is generally not recommended unless specific conditions are met. You should only consider this project if the tree is small (e.g., under 4-5 inches in diameter and short enough that you don't need a ladder to reach the branches), and you are experienced in handling a chainsaw. The tree must also be located far from any power lines, fences, homes, or other structures. Even for small trees, the work can be dangerous, and it's always advisable to have a spotter to ensure the tree falls correctly and no branches fall on you.

For any tree that is large, requires a ladder to access, or is near electrical lines or structures, you should always hire a professional. Attempting to remove a large tree yourself is extremely dangerous, poses a risk of serious injury, and could result in significant damage to your property.

Before any tree removal, it's also important to check your local and state regulations to ensure the tree is not historic or otherwise protected by your city.

Yes, it can be good to remove dead branches from trees. Dead branches can lead to rot in other areas of the tree. They can also cause damage if they fall on a house, shed, fence, car, pool, or other structure or property. However, it’s important that dead branch removal is done safely. If the branch is high in a tree or requires a lift or ladder to access, consider calling a professional tree removal company, as they will have the experience and equipment to do the job safely.

In some states and municipalities, you will need a permit to remove a tree on your property. In many cases where permits are required, a tree must reach a maximum height before a permit is required to remove it. You can either ask your local building department or a tree removal professional if you’ll need a permit. If you do, you can expect to pay between $50 and $150 for the permit alone. Your tree removal company should pull the permit for you and include the permit fee in your total.