First off, while the media is in a bit of a frenzy over cuts made this week all over MLB, the Atlanta Braves truly didn't do anything unusual. Most teams really didn't, either.
There was an unconfirmed report on twitter announcing that Atlanta had made 50 player cuts from the minor leagues. I won't repeat the source of that, for it now appears to have been a completely overblown number.
Full credit to JJ Cooper of Baseball America for not only getting the number of actual cuts - thirty - but also in identifying the players involved.