Your Mailbox Is Approaching Its Quota!!

I'm getting this message regularly.  For some reason my folders in Outlook are synced to folders in Cox Mail.  Whenever I intentionally save an email in an Outlook folder it saves it in Cox Mail.  I do not want to delete these emails. They are important to me.  I'm afraid if I delete emails from my Cox Mail folders they will also be deleted from my Outlook folders.  How do I un-sync my Outlook from Cox Mail so I don't exceed my Cox Mail quota?