There are essentially two ways to get hold of source material broken down to stems or tracks.
a) Negotiate with the record company for the rights to use, pay the fee, agree the royalty split, they will send the source material.
b) be employed by that company as a remixer. Same as a) but you will probably be working for a fixed fee, so it costs you less initially, but you don't get the chance to 'make it rich' if it's a hit.
c) Some artists intentionally release their material in stems or full multi-tracks, to encourage remixers. There are sites dedicated to this. These are likely to be under some type of Creative Commons licence. [This bit is all a bit new for an oldbie like me, so I'll let someone else fill in the details ;)
There are a lot of stems & multitracks that have 'escaped' onto the internet.
a) Pretty much everything done for Guitar Hero & similar games has been posted as stems, in the game's format; five stereo stems - vox, guitars, bass, drums, other
b) Some very famous tracks have been 'acquired' from the multitracks & posted up. From Bohemian Rhapsody, Ziggy Stardust to Superstition ... & a lot more.
Re-use anything from category 2 at your own risk - the lawyers will be beating a path to your door.
Actually, there's a late 3rd option...
- Do a remix using whatever you can find, basically 'steal stuff'.
Put it out as a limited white label to make it untraceable [or not worth the effort of the lawyers trying to actually prove it was you, as there is no money involved.]
If it gains some traction on the dance floor, replace all the illegal bits with legal re-creations, tweaking to avoid copyright issues.
Release version 2.
Real-world example of 3.
Anaya Day - Nasty Girl
Original "Bootleg Mix" -
containing some pretty obvious M Jackson samples.
[This version may be subject to takedown at any time in future, it was not posted by the record company or remixers (who are friends of mine)]
Official release with 'legal replacement' -
The idea that you can remove or extract specific parts of any stereo recording to re-use yourself is what I would call a 'holy grail for the misinformed'.
It's possible on occasion to extract some parts using techniques such as phase-inversion, but the chances of success are very small & even if it works you don't really get to choose what you can extract this way.
Consider this task the equivalent of unbaking a cake & forget it.
It would also land you squarely in category 2, with the lawyers after you.