You can put the tool on top if it's smaller than the mirror. If they're the same size, then the tool needs to be underneath.
This video shows the use of a sub diameter tool on top.
https://tinyurl.com/2p93sucv
Better machine designs will also move the tool using two cams at right angles to drive the tool left/right & forward/back The stroke lengths can be adjusted.
With this design, the overhang amount will need to be frequently adjusted.