Depends on OS version..
Remove email accounts
When you remove an email account, the account’s messages are removed from your Mac. Copies of messages remain on the account’s mail server and are still available (from webmail, for example).
Important: If you’re unsure whether messages you want to keep are still on the mail server, move or copy them to a mailbox stored on your Mac (the mailbox appears in the On My Mac section in the Mail sidebar) before you remove the account in Mail.
- In the Mail app
on your Mac, choose Mail > Settings, then click Accounts. - Select an account, then click the Remove button
. - Note: If the account is used by other apps on your Mac, you’re asked to remove the account in Internet Accounts settings. Open System Settings > Internet Accounts, select the account and turn Mail off.