Removing a mail account on your phone shouldn't depend on Cellular or Internet Connectivity. If it is a email account using the built in mail app, then just delete from the settings:
- Go into Settings > Mail (might be called Mail, Contacts and Calendar on older iOS)
- Click on Accounts, select account you want to remove and at the bottom it will have a remove option.
If you have tried that, what is the error your getting?
If the account isnt there then it might be using a different mail app from the App Store, in which case you would have to remove it from the app not the phone.