First you have to login to your Dedicated server as root via SSH. Then browse to the /home/USERNAME/mail/YOUR_DOMAIN/MAIL USER/ folder.
In it you will find folders named cur and new. The "new" folder contains all the unread messages you have in your inbox and the "cur" directory - the ones you have already read. Each mail presents a file in those folders. You can delete the ones old enough in order to free some space for your mailbox.