I had this problem too, so I called Apple.
The problem seems to be iCloud related.
The cure was to quit out of Mail,
Open System Preferences,
Open iCloud Preferences,
Attempt to sign in to iCloud,
If that fails, choose sign out,
You should finally get to the iCloud Peferences page and probably see that "Mail and Notes" is unchecked.
If yours behaves like mine, Mail should now be working.
No, I don't understand what happened. There is a cloud over my eyes.