Well, yeah, and no... There's a few levels of scope involved here. Even when saying the edge separates the bonds of individual molecules, I think people are getting a little ahead of themselves, because much blunter knives can also cut material. It could have something to do with the pressure and compressive forces and is probably some type of thermal reaction that allows the region underneath the edge to become much more excited then the region surrounding it, allowing it to be pushed out of the way, and the rest of the material wedged apart in a mechanical function. Anyway, I'm just offering my own conjecture here, but I think it's much more of a mechanical operation ( planes and wedges ) that takes advantage of the extreme pressures created at the edge.
I think it's more likely a thermal reaction. That much pressure and compressive forces would definitely cause heat exchange, so maybe that just is indicative that the edge and pressure it's creating is actually exciting the material enough to break apart and generate heat... That in itself would have an interesting dynamic at the atomic level. I just don't seeing it having much to do with electrons repelling each other, because that's more along the lines of radiation, fission, fusion, etc. It's more likely to me that at an excited level, the electrons that form the bonds between the molecules become so excited that they cannot maintain, and they separate.
I've really never thought of an edge at this much of a scientific level before though. I wonder if anyone has actually done some real research into the science of a "cut". Is any matter actually "destroyed" (i.e. changed to something else through a thermal or other reaction ) or is it literally all just separated at the molecular level like is the general consensus?
trick question