It seems that the controller is located right on top of the numpad section, so if you cut it, all the traces that are going onto the chip are lost.
So no you can't cut it like that and hope for it to work, there should be a way to do it, but I don't know enough electronic to help you.
The idea I'm getting though is that as long as a trace is intact, it's keys will work, no matter how many other traces have been cut, is that correct?
If a trace is intact, everything connected to it will be operational.
HOWEVER, if you cut traces that are associated with the controller, the switches might work but the keyboard won't.
FURTHERMORE, if you cut out the 60% part, the rest may not work. The firmware operates by scanning each of the traces for changes in a matrix style array. If parts are missing, the controller may believe that they are always on or always off (depending on the chip).
Will it work if you proceed to **** it up? Probably not. The arrows, pgup cluster, and TK are all connected with the alpha set in the 'row' direction and the F# keys are connected to the 'column' part of the array on these boards.
Are you just trying to make a 60% board and harvesting from this one? That might not be easy either because each end of the column and row (probably now on the edge of your cut) will have to be directly soldered to a wire which goes to a new controller.