Sceneray

Sorry if im talking at the wrong place, but as the title said, is it possible to change the object cuts to a specific one when subdivison surface is on, im trying to make something like the knife cut will be added onto a object when subdivison surface is on and it will be gone when subdivison is off, but i don't really know how to do, anyone knows how to make?

Anyone knows why there are some lines between the cubes, sorry im new