How do I delete the Mail App from my Mac computer?

No, de-activating the account will not delete the old emails - it will just prevent it from downloading new ones. You will still need to delete the old emails. Got to your User account (Home icon) > Library (it is now hidden: hit Option key while clicking on Go in menu bar) > Mail and navigate to the folder that has all your emails in it. Do not throw out the folder, just the emails - they should end with .emlx. There are probably several folders - check each one. Drag all the emails to the trash and empty.

Do a Finder/Spotlight search for folders named " INBOX.mbox " - open it > Select All > press ⌘ Command + delete > press ⌘ Command + ⇧ Shift + delete to empty the Trash

If ypou really want to delete the Mail.App, drag it to the Trash & empty

or

Select " Mail " in the Applications folder > press ⌘ Command + delete > press ⌘ Command + ⇧ Shift + delete to empty the Trash

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You might want to reconsider: simply do delete the emails, but it is generally not recommended to delete an application which was installed as part of the OS.

The reason you are getting the emails is because you have set up Mail to fetch your Gmail emails. If you want to open the Mail app and go to Preferences > Accounts, you should see your Gmail account listed - if it is, simply highlight it and click the "enable" to un-enable it. If you want to get rid of it forever, click the minus sign at the bottom. As long as Mail is not configured to fetch the emails, it will not do so.

Launch Mail. Mail > (upper menu under Mail) Preferences > Accounts > highlight the account and delete or deactivate it by hitting the minus button below or simply UN-enabling it. Note the checkmark next to "enable this account" - uncheck that.