This is quite late but I'm mainly replying to help others with the same question/problem who may come across this.
To access your save games on a Mac: right-click the "Alpha Centauri Alien Crossfire.app file", and then click "Show Package Contents". From the resulting new view/window, work your way down through this folder tree (by double-clicking each subsequent folder in sequence):
drive_c\Program Files\GOG Games\Sid Meier's Alpha Centauri\saves
That's it...they should all be there, and can be treated as any other files using Finder.
P.S. Just to add, as far as I know, the previous advice given above is not correct and will not help whatsoever (nothing to do with Mac OS version). The answer involving Boxer only applies to older DOS games (which Alpha Centauri certainly is not).