It isn't possible to unsubscribe a student from emails or SMS, only guardians.
This is because if you are communicating with a group of students, every student in that group likely needs to know the information being shared.
What if they have left the school?
If the student has left the school and you don't want them to receive any communications, you could remove their contact details from the Contact Details section of their profile. You can always add contact details again.
Top Tip: Make sure you aren't using any third party apps that will rely on pulling this email address from Arbor.