How do I prevent Drupal from sending an email to the admin every time a new user is created
Do the email sent to the admin have the link to activate the user's account?

If so, go to: example.com/admin/config/people/accounts

Check the REGISTRATION AND CANCELLATION paragraph (should be the 2°): if Visitors, but administrator approval is required is checked, every time a user create an account an email is sent to the admin to let him approve/refuse the user new account.