You cannot just turn off mail notifications for a particular user in CLM but you could do some workarounds.
Make sure that when the user is added to a document it is as a silent user or if they really do not have to receive any email from CLM you could just change their email address in their user profile to a dummy one so it will never be sent to this person.
What about a custom rule on the Mail Configuration object:
name.surname@co.com=delete;@all=send;
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