Any cutting of tree roots can hurt or kill a tree, which is why it's recommended you don’t do it unless the roots are damaging or invasive on a nearby structure like your home. You should never cut more than 15 percent of above-ground tree roots at one time. If you have any questions about cutting tree roots, contact your local arborist.

There are a few instances in which removing a tree is the best option. You might do this if the tree looks to be a major danger—potentially falling onto your home, your car, or other parts of your property—or it’s diseased beyond repair. A tree that is growing too close to your house might need to be removed to prevent mold growth.

You can use a felling ax to chop down a tree by following the same prep and steps as a chainsaw, but be prepared to use some muscle. For trees bigger than 7 inches in diameter, it can take some time and serious strength to cut down a tree using just an ax. 

Late winter is ideal, but if you’re pruning apple trees in the spring, prune them as early as possible in the season. You want to ensure your tree is just creeping out of dormancy and hasn’t started pushing out new growth. If you prune your tree too late into spring, you generally won’t see results until the following year.

That said, there’s no pruning season for unhealthy growth. Remove dead, dying, or diseased branches as soon as you notice them, regardless of the time of year.