There’s a known issue with the StarCraft II Beta Mac client that is causing the game to generate extremely large crash logs if the client does crash. These may take up an unnecessarily large amount of harddrive space and can be deleted safely if they do exist. Crash logs can be found here: /Users/<username>/Documents/Blizzard/StarCraft II Beta/GameLogs/

Patch 12.1 will be released within the next day or two to resolve this issue.