API apps cannot be deleted.
If you want to ensure that access to your app is disabled, Vimeo Support can deactivate your application on our backend. Contact Support and provide your app id or client_id and a member of our developer support team will assist.
Developers can deactivate any tokens they have generated by making a request to the revoke token endpoint. Read more on the Vimeo Developer page at 'API Apps: Delete an access token'.