What are three ways a fossil can be destroyed after it has formed.

Ossils can be destroyed by erosion after they form. Rocks can be weathered and broken up by wind/water/ice, and the fossils can be broken up as well. 

Rocks that contain fossils could be metamorphosed. If mild, the fossils will be visible but stretched. If pressure and heat is intense enough, the fossils are obliterated. 

Also, many marine rocks (and any fossils they contain) are subducted at plate boundaries, and that will melt and destroy the rocks. 

Those would be the main ways that fossils get destroyed!

There ya go. :)