If you have ever watched a tree grow from a small twig to a large, mature tree you know that cutting a tree will affect the roots. If you cut a tree and the roots become too weak the tree will fall and can cause property damage or even kill a person. There are steps you can take before you cut a tree to keep the roots healthy and to make sure the tree doesn't fall.
To determine when to cut a tree will the roots die you need to look at the structure of the tree. Look at the trunk, the branches and the roots. A strong stem is going to remain intact as long as the tree isn't cut through and there is no other way the branch can support it. If the tree has branches that break off then the tree will eventually grow without any support. When you cut a tree you can't just pull the whole thing out and if you don't do it right you could seriously hurt the tree's roots.
You will want to make sure you only cut the portions of the tree's roots that are growing. If you cut a branch and end up killing part of the tree's roots you may have to remove the dead part and replace it with new growth. You can usually identify a broken branch this way and if you have time you can fix it. It's often better to cut off a portion of the tree's trunk and replace it than to chop away the whole thing. This way you can be sure the tree will still have some of its nutrients in it when it grows.
Now that you've got rid of the tree's roots you should be able to see what part of the tree needs to be removed. Look at the base of the tree and see where the trunk meets the ground. You will usually know what needs to be cut off when you notice that part of the tree is no longer growing. If the trunk looks distorted or if it looks like it has been bitten by something, then you need to take the root ball apart. This is especially true if the tree you chopped has an odd shape to it.
If the base of the tree is still intact but the part that was cut off has lost most of its leaves then you need to get it to grow again. You can do this by carefully digging around the base and putting soil on it. Make sure to place a trellis in the hole for support so the tree's roots won't be thrown off. Once the soil is in place you can place the tree in the hole and tie a ribbon of burlap around the base. Burlap will help keep the roots alive as they work their way back to the tree's roots.
It isn't very often that people need to cut down a tree. Usually trees are chopped down because they are in danger of falling and injuring someone. The person doing the chopping will have to make sure that they are keeping themselves out of the way of the falling tree. If you don't have any plans of cutting down a tree this year then you may want to consider taking some time and finding out how you can save a tree that is going to fall.