If your mailbox is full, or you are using a lot of disk space for it, it's possible your mail client (Outlook, Thunderbird, etc.) is not removing the email from the server when it downloads it. You want to be sure that the mailbox is set up to NOT leave a copy on the server. Otherwise, the mailbox can fill up rapidly. Once full, you will not be able to receive email until you clean it off or increase the mailbox limit.
It is also possible that you are forwarding your email. If you are, be sure that you have ONLY a forwarder set up in cpanel. If you also have a mailbox set up, it will both forward and save a copy on the server.
We can wipe the entire mailbox clean for you if you are sure you already have gotten all of your email. We can not, however, pick and choose email to delete. If you need to do that, you will need to log into webmail (found in cpanel or at yorudomain.com/webmail) and manually remove email.