Hi Gray,
A lot of the free / illegal site shave been shut down, like beemp3 / piratebay etc. You can download Youtube clip converter, simply copy and paste the music video URL and drop it in the required place, you can then select the conversion format, so if you want the music only, then select mp3 and 'Download' - You select the location for the file to be stored - JD. You can split a video / audio file in most movie editing software, but it's less fuss if you just download what you need.
http://www.clipconverter.cc/ As said, you will get a message from Ytbe saying third party content and blocked in some countries and it won't play on all devices.
Here's one that someone made earlier:
https://www.youtube.com/watch?v=u3d7JrtILcQHope this helps.