I think I have found the answer! I have had this problem ever since switching from Blackberry a long time ago. Seems like mail sits on your phone forever, taking up space for fear of the messages being deleted from your server. I tested this and it works for me:
DO NOT DELETE THE EMAILS FROM YOUR PHONE'S INBOX OR TRASH!!! ESPECIALLY DO NOT MOVE THEM TO YOUR TRASH IF YOU WANT TO KEEP THEM!!
Leave them there (inbox) temporarily. When you have the chance, log in to your email from your pc or laptop. MOVE the emails you want to keep to the appropriate folder/subfolder (Clients, Marketing, etc). After you have MOVED the messages to a folder other than the INBOX or TRASH on your computer, check your PHONE email (and "refresh" if necessary). As soon as it syncs, those messages are no longer on your phone, but are safely stored on your server (pc/laptop).