Luckily I had a 2nd SIM card at home, when I was able to test. Those simcard (for my cheap Nokia cell phone sports) is rarely in use and if the Broken would have gone, it would not have been so bad.
I had in mind, since the cutter but cut off on one side of a portion of the chip. But this is apparently not a problem.
After I had reduced my sports cell phone SIM card (and had broken with the nail file the edges) I could into operation (thanks to the supplied adapters successfully iPhone 4S I then could the reduced SIM card and immediately insert in my sport phone. Also it worked properly).
So I then dared me to my actual SIM card which was to downsize and there I was also successful :-)
(Note: My provider is Orange Switzerland (prepaid))