Deleting an email account removes all emails from the device
- Find and tap the "Settings" icon.
- Tap on "Passwords & Accounts", older iOS versions it will be called "Mail" or "Mail, Contacts, Calendars".
- Select the email account you wish to delete/remove.
- Tap on "Delete Account".
- Confirm this by tapping on "Delete Account" or, sometimes it may say, "Delete from my iPhone".
This will remove all emails from your device, this means you will no longer see any emails in the Apple mail app. This may also remove calendars, notes, to-do items and contacts that use that account.
Please bear in mind that sometimes it can take a little while to wipe the emails.
This doesn't delete the account itself from the email service you're logging into: IMAP, POP, Exchange, Google, Yahoo, it also doesn't delete emails from the server. (Unless you have deleted them prior to the removal of the account)