Screen mirroring does work but it's quite complicated and you need to be at our PC for it to work. It's much easier just to use a non-root screen recorder. You need a PC to complete the installation but thereafter you can record without the USB cable. There are a couple available on Android now. I recommend Recordable:

http://recordable.mobi/app

... but you can see the full list here:

http://recordable.mobi/compare