If you no longer want to access your Emails from the MacBook, you can either remove the Email Account from the Mail App or temporarily disable the Email Account on your Mac.
When you delete an Email Account from Mac, all Email Messages associated with the Email Account will also be removed from the Mail App and you won’t be able access them from within the Mail App.
However, the deleted Email Messages will still be available in their original Mail Servers (Gmail, Outlook, etc.) and you will be able to access them by logging-in to your Email Accounts.
Delete/Disable Email Account on Mac
If you are only interested in preventing Emails from appearing in the Mail App on Mac, you can temporarily disable the Email Account in the Mail App.
In this case, the disabled Email Account will still remain associated with the Mail App and you will be able to get back all your Emails on Mac by enabling the Email Account in the Mail App.
The other option is to remove the Email from the Mail App on your Mac, in which case you will be required to go through the process of adding the Email Account to Mail App, in case you want to see your Emails on Mac.
1. Remove Email Account from Mail App on Mac
If your Email Account is not currently being used by other Apps (Contacts, Calendar or Notes), you can remove the Email Account from within the Mail App.
1. Open the Mail App on your Mac > select the Mail tab in top-menu bar and click on Accounts.
2. On the next screen, select your Email Account in the left-pane and click on the – icon.
3. On the Confirmation pop-up, tap on OK to confirm.
Once you click on OK, the Email Account and all its Email Messages will be removed from the Mail App.
Remove Email Account from Mac Using System Settings
If your Email Account is being used by other Apps (Notes, Contacts and others), you will be prompted to remove the Email Account using System Settings or System Preferences.
1. Click on Apple Logo in top-menu bar and select System Settings in the drop-down menu.
2. From the System Settings screen, go to Internet Accounts > select your Email Account in the left-pane and click on the Minus icon.
3. On the confirmation pop-up, click on OK to confirm.
The selected Email Account will be deleted from your MacBook.
2. Temporarily Disable Email Account on Mac
As mentioned above, the other option to prevent Email Messages from appearing in the Mail App is to disable the Email Account on your MacBook.
1. Open Mail App > select the Mail tab in top-menu bar and click on Accounts in the drop-down menu.
2. On Internet Accounts screen, select your Email Account in the left-pane and uncheck the little box next to Mail in the right-pane.
3. After this, make sure you quit the Main App.
Now, when you re-open the Mail App, you will find it empty with No Emails in it.
At any time, you can get back all your Email messages in the Mail App by opening the Mail App and going to Mail > Accounts > Your Email Account and checking the little box next to Mail in the right-pane.
Note: You will need to close and reopen the Mail App to see all your Emails.