Trying to remove a tree on your property can often be a mistake; the work is typically more dangerous and complicated than you realize, and many homeowners wind up damaging their property during the process. Note a few tree-removal mistakes that are very common with homeowners so you can avoid these yourself or determine whether you should call a professional tree-removal service instead.
1. Not trimming the tree before removing it
Since you want to cut down the tree and pull up the stump, you might think there's no reason to trim the branches at the top. This can be a mistake, as those branches can pull the tree in any number of directions and also make the tree heavier than you realize so that it falls before you expect it. The branches may also be wider than you calculate and hit a garage, parked car, or power lines in their path as the tree topples.
2. Not knowing how to use a chainsaw
A chainsaw is a very dangerous tool, and it should never be used by anyone without experience, no matter how "handy" they are with other types of saws. If you do want to use a chainsaw on your tree, it's good to practice with it on some thick branches attached to a sawhorse of some sort. You can then get accustomed to the kickback of the saw and how much pressure you need to apply to make the cuts safely.
3. Not considering how the tree affects other vegetation in your yard
Tree roots can hold moisture in place and keep other vegetation healthy. Rather than removing the tree, you may want to keep it in place and allow it to grow, if possible, so its roots stay intact. Otherwise, you might want to consider changing the slope or drainage of your property so that other vegetation doesn't wither and die once the tree is removed.
4. Trying to just rip the stump out of the ground
Tree roots can be very deep and far reaching, and there may be more to the buried stump than you realize. Trying to just wrap some chains around the stump and pull it out of the ground with your truck can mean actually doing damage to your truck rather than the stump, and it can also mean accidentally pulling up plumbing pipes or buried cables and power lines. If you haven't cut into the stump to see how deep it goes and don't know how far the roots extend, it's probably best to leave this part of the tree removal process to professionals.