Both -tome and -tomy are Greek combining forms that lend new meaning to Greek or Latin words with which they are combined. Both combining forms are from the Greek word tomē that means "cutting," the action of cutting." They are distinct from each other in that -tomy indicates the area where a surgical cut will go, as in appendectomy, while -tome indicates the tool, or instrument, with which the surgical cut will be made, as in micrtome.
The suffix -tome refers to a surgical instrument used to cut into or remove a specific anatomical feature. The suffix -tomy refers to the actual act of cutting into the organ or area.
For example, a tonsillotome is an instrument designed for removing part of all of a tonsil. A tonsillotomy is the actual surgery involving an incision into, or removal of a section of, a tonsil. Just for good measure we also have the term tonsillectomy, which means the complete removal of the tonsil.