Introduction
Open the Settings app. Tap Mail > Accounts > email account that you wish to delete > Delete Account.
Instructions
1) Open the Settings app.
2) Tap Mail.
3) Tap Accounts.
4) Tap the account that you wish to remove.
5) Tap Delete Account.
6) To confirm that you wish to delete the account, tap Delete from My iPhone or Delete from My iPad.
CAUTION: Deleting this account will remove all associated email, contacts, calendars, reminders (tasks), and notes from your device. This cannot be undone! However, the associated account and any settings/data stored on the servers for that account will remain intact. If you are unsure whether you wish to proceed, tap Cancel.
7) Please wait while your iPhone or iPad removes the account. This may take a moment depending on the amount of data contained within the account.
Outcome
Your account will be deleted from the mobile device.