Absolutely. There are a number of guides & videos on how to do it. AFAIK, you can also cut full size and micro down to nano. There are a number of SIM cutting tools available online for cutting a full size SIM to either of the smaller variations.
I still always found it easier to drive down the street to AT&T and get a new SIM. I was afraid I'd screw it up cutting it. -- QUAD!!!!