My ornamental plum tree has a fungus growing on the main trunk and other branches; can I shave it off?
The part of the fungus you see is the fruiting body (mushroom-like spore dispersal organ), the growing body is the mycelium which is deep inside the woody tissues. It doesn't do much good to shave off the fruiting body, it would be mostly for cosmetic reasons.
From the photos this tree appears to be in bad shape, poorly pruned, sunburned and with extensive decay. The fungus present appears to be growing out of dead wood and cavities, and not affecting the living tissue. But its hard to see what's going on without photos of the entire tree.