Well, I know a guy who has done it. He has his own record label - and there's the secret. If you are somewhat established in the biz, you can ask the record label of the artist who you want to remix for separated tracks on DAT or ADAT. If they feel you can produce something interesting, and that you're somewhat well known (they're not going to give these precious tracks to somebody if the remix is only going to be heard in the remixer's bedroom), then they will oblige your request.

The only alternative for "nobodies" is to cut up the original track (the full mixed version) and do your best to filter out different elements (i.e. pull down the bass and some of the highs to get the vocals). But this method leaves you with pretty lousy sounding samples to work with. Of course, this could prove to be an even more interesting effect than having the clean, separated tracks.

Another route to try if you want to build a portfolio of work (to show the big labels what you can do) is to hook-up with smaller labels and artists and ask to remix their tracks. You are more likely to succeed in obtaining separated material as a "nobody" if the track your requesting is also by a "nobody." If your good, you might get asked to produce some more remixes by that label, or eventually by bigger and bigger labels.

BTW: When I say "nobody," I just mean you ain't no Puff Daddy, so forget about calling David Bowie to get some tracks to remix!