If you notice "big mushrooms" growing out of your tree, you should take notice. Known as brackets, these fungal growths are a sign that your tree has a serious fungal infection in its interior. By the time the brackets appear, the tree is usually too far gone to save, and you really only have two options when it comes to dealing with the disease.
Option 1: Have the brackets trimmed away to prevent spread of the fungal disease.
The brackets are the fruiting bodies of the fungus, which means that they spread fungal spores. This is a concern for other trees in the area, which may become infected if the brackets are left in place; most fungal diseases infect multiple species of trees, so it's not just your own tree type that's at risk.
If the tree is in a remote area and you are not concerned about property damage if it should fall, having the brackets periodically trimmed away and leaving the tree to slowly die on its own is an option.
Keep in mind that the tree will die eventually, and at that point, you will need to have it removed (whether it falls on its own or has to be taken down). However, simply trimming away the brackets is a good temporary fix if you cannot afford to have the tree taken down immediately and want to protect other trees in the area.
Option 2: Simply have the tree taken down.
Since the tree is on its last legs anyways, it may be wise to just have it taken down. This is certainly a good choice if the tree is near your home or another structure that could be damaged if the tree were to fall. The internal fungus weakens the tree substantially, and there is a chance it could become so weak that it falls over or major branches fall off.
If you choose to have your tree removed, make sure you have a professional tree removal service handle this task for you. He or she will know how to handle the brackets and infected wood to minimize the spread of fungal spores to nearby trees in the process. Depending on which fungal disease is infecting your tree, the wood may need to be disposed of carefully (it's usually burned) to prevent spreading infection.
If your tree develops fungal brackets, don't ignore this symptom. It's a sign of a serious disease that will kill your tree, and leaving the brackets puts other trees, both on your property and on neighbors' properties, at risk.