That's no problem. What you see on the surface of the SIM card are just electrical contacts which can be cut as long as the signitifcantly smaller chip below is not damaged. This x-ray image shows how small the actual chip is:
I've actually cut almost my whole SIM collection to match the 3FF (third form factor = microSIM) and some also had these giant contacts.
However the bad thing about nanoSIMs (aka "4FF") is that you will not only need to cut the old formats to match this new format but you also need to file down half a milimeter as nanoSIMs are thinner.