. What exact Mac model do you have?. What exact Mac OS are you running?. For Outlook, do you have Office 2008, Office 2011, or Office 2016? I have used all 3, but am most familiar with Email cleaning for Outlook 2011 and (currently) Outlook 2016. Have you ever done any disk cleanup/maintenance/repairs, from a software perspective?. Are you making backups to an external device?
And if so, what software are you using for that? Now, regarding Outlook, I assume you have deleted Emails in the past.
Also, you should consider deleting any you do not need. For Outlook 2011, there is a way to rebuild its database (ie, Identity 'file') to permanently remove deleted Emails. (For Outlook 2016, the procedure is different).
In Outlook 2016, go to the File tab, and click Tools > Clean up old items. In Outlook 2010 and Outlook 2013, click File > Cleanup Tool > Archive In the Archive dialog box, select the Archive this folder and all subfolders option, and then select a folder to archive. For example, to archive Outlook calendar, select the Calendar folder. This feature is not available right now. Please try again later.
Here's a link for outook for mac 2016 database rebuild: If that also does not work then you can opt for third party apps, one which is making headlines now a days is mail backup x, check out one of the articles: Please note that all the third party apps are paid. First go for the manual procedure.
I hope this helps.