Irrelevant of the Email client that you are using. My suggestion is that just go the mail options or sync option in the Program that you're using to download your emails to. Go to a preferences/options/accounts tab there and just delete the email address specified there. After that you can delete the whole account in the program.
It would be nice to know what program you are using so we could give you a stepwise deletion of Mail accounts from the Program.
If you understand that an email client is like Outlook Express, MS Outlook, Bat, Thunderbird etc etc. These are the names of the programs that are used as email clients.