I have been struggling with this problem for years and I am hoping that someone out there has the answer. I can sometimes do it but more often than not I can't. I usually end up breaking them into a thousand pieces. Is there a trick to it?
You get yourself a cake leveler. Wilton has a cheap one - only about $5 that is good for small cakes - up to 10"(?)
Or you can invest in a much more expensive one for bigger cakes.
Yes, there are ways to do it w/o a saw but this is sooooooo much easier.
If you are asking how to get the two cut pieces apart then simply keep a cake board about the same size as the one you are cutting (torting); lift a little of the cut cake, slip the board between them and push it onto the board. When ready to replace the cake just jiggle the cake off onto the other cake. If you want, cover this board w/Contac Paper; it will keep longer as you can use a damp cloth to wipe off the crumbs and it makes the cake slip on & off easier.
I find that freezing the cake layers for a few hours before torting them also helps a lot.
Cake levelers are the best way. And they're easy to use. I have heard that unflavord floss works too, but I have never tried. Also, don't try to cut them too soon after cooling. They should set up a little bit.
Enjoy your flat layers!