Remixing is a little bit more complicated than that, you'll have a tough time removing tracks. If you're interested in remixing a good place to start would be to get some acapella tracks (just the vocals). You'll have to try and find the acapella of the track you want to remix. The legal way of obtaining acapellas is to get 12" singles, which will usually have acapella tracks on them. Then you just need to import the acapella, figure out the bpm and get cracking. The other way of getting acapellas is not strictly legal, but if i give you the words "google", "remix" and "acapella", i'm sure you can take it from there. As long as you don't try and sell anything for profit there's no reason for anyone to come knocking on your door.