Full stems available for only Monster and Paparazzi AFAIK; I have them here:
http://thepiratebay.ee/torrent/5619510/Lady_Gaga_-_Track_Stems_-_Monster_%5BFLAC%5D
http://thepiratebay.ee/torrent/5619439/Lady_Gaga_-_Track_Stems_-_Paparazzi

However, there are lots of a capella and instrumental breakdowns available.
Some are official, some are fanmade / filters. (I didn't do any of the filters; I just collected them) Some of the unofficial files are better than others.

The folder structure puts each song's pieces in a separate folder, but the album tags are "Lady Gaga A Capellas" and "Lady Gaga Instrumentals", as appropriate.

The artist tags are all "Lady Gaga", and the genre tags are all "Pop".
For date tags, I used the date the overall song was initially released, not necessarily the date the a capella or instrumental came out.
No track-number tags.

There are a few FLACs, ripped from CD singles on which they were released, but most of these are are just MP3s. While all of the FLACs are official, not all of the MP3s are unofficial.

For some of the songs in question, I don't have the a capella AND the instrumental, but I included what I've got.