The easiest way to do this (credit to Harmen Utrecht) is as follows:
Problem: Mac Mail keeps recovering same messages over and over again.
Go to Mail Preferences.
Select the mail account involved.
Go to tab Advanced.
Under "Keep copies of messages for offline viewing" select "Don't keep copies of any messages".
(Don't worry, they are still on the server.)
If needed: Delete the problem messages from the Recovered Message folder.
If you want, go back into Mail Preferences and reset the choice back to the old "Keep messages for offline viewing".
Then, everything will be back the way it was, but the problem messages won't come back.