You can unsubscribe a guardian from mail merge emails, SMS, letters and in-app messages. This will not prevent them from logging in unless you disable access. Please note that when doing this, they will still receive communication sent directly to them from the guardian or student profiles.
You can see how to do this in bulk here: Updating Guardian Contact Details in bulk
Or for individuals, you can also go to their guardian profile and click the relationship with the student in the Linked Students section.
Tick the box to unsubscribe them from communications, then click Save Changes. You'll need to repeat this or each student they have been linked to.