On Andy Rehfeldt's (the guy that made those kind of videos) website theres a FAQ-Section which appears to have an answer to your question: he just uses google.
Q. How do you get the isolated vocal tracks that you use in your videos?
A. One word – GOOGLE. I just search for them. The acapella vocals (as they’re called) are often released to DJs so that they can be mixed and re-mixed live in clubs. Those acapella vocals often find their way onto the internet and are fairly easy to find if you look! I don’t use any special software, I just find them already split out.