How to disconnect apple id from one user on macbook

I set up a second user on my MacBook Air laptop and accidentally used the same Apple ID as I had used for the original user on the laptop. Is there any way to disconnect that second user from my Apple ID without messing up things for the other, original user account? What I would really like to do is to have the second user not be connected to any Apple ID. That user will just be used for connecting to the internet. No need for messages, mail, etc.

Thanks.