My external Passport drives started doing a self shut down after a few seconds of connecting to my Mac. After much agony and many wasted hours, I finally resolved the problem. As of today, 8/26/2015, the problem is the WD Utilities software update ver. 126.96.36.199.
To fix the problem:
Remove both WD Utilities and WD Security from your Applications Folder. Go to Finder, Applications, and select both apps and delete.
Restart your Mac.
Reinstall WD Security only. Update to latest WD Security version if you like.
As for now, Do NOT install WD Utilities app.