You can use the cPanel Backup Wizard to do a full backup of your site and email, but it would be a good idea to download it to your local computer and extract the contents to see if the mail is actually being backed up.
Recently we had migrated a customer from SiteGround (cpanel host) and they had edited the cPanel config so it did not backup the mail. We had to manually move the mail folders to our server.
If the main disk consumption is from mail. It would be best to pop the mails using a mail client like Thunderbird by disabling the option " leave a copy of mail in server". The main disadvantage is if for some reason your local machine get attacked by any of the virus you may loose the entire mail.
So it would be best to schedule a backup generation of account files + email periodically( say weekly) and then download the compressed backup file locally and schedule a cron job to clear all mails which are older than a specific time period.