I have been having this problem all day, and I finally fixed it thanks to a couple of posts I saw elsewhere on here and adapted to my specific version and installation of Office 365 (64-bit) on Windows 8.1 (64-bit).
cd /d "%SystemDrive%\Program Files\Microsoft Office 15\root\office15"
Groove.exe /clean /all
The /clean by itself didn't work. I really needed the /all parameter, which I found in a forum search, but it was not for my version of Office. Now, I am guessing that anyone using the recommended 32-bit version of Office 365 will probably want to do this instead (just a guess, so don't get mad if it doesn't work as I don't have that particular version installed):
cd /d "%SystemDrive%\Program Files (x86)\Microsoft Office 15\root\office15"
Groove.exe /clean /all
Hope this helps someone. It's too late for the chunk of hair I pulled out, but the rest of my head is now safe. Best wishes.
Byron