Can I cut the pin holes off of my Arduino board?
I guess that one could cut (or hone down) parts of the PCB. Obviosly this process devoids the warranty and there is the risk of damaging either the board or some components on it (i.e. by holding or clamping it during the process). 

I would not expect any other wiring besides those connecting the pins to run in this part of the PCB. The reference layout (see board layout and using Eagle (free version)) - if the clones follow that layout - confirms that there are no other traces there. So it is mostly important to not cut any other traces and remove any chippings after the cutting to avoid short circuits.

If in doubt buy two or three boards ;) to try and repeat the process.