I would not want to overload an already full teacher screen with even more buttons. Hence my initial thought was, in these cases, you could simply click the "Edit slot" button, and remove the individual student appointments that are no longer required.
However, you say that this has not worked for you, giving you an error "You can't start an empty appointment slot in the past", is that correct?
This seems like a bug to me. However, I tried to reproduce it on the latest version of Scheduler, and for me everything seemed to work out fine. You can tick the "Delete this appointment (when saving the form)" checkbox for one student (or more), and the appointment will in fact be deleted. The error message is shown only when you try to delete *all* appointments in the slot, thus leaving it empty, but i understand that that's not the case you're asking about.
Hence the problem might have to do with the Scheduler version you are using. The edit screen has changed several times, and the method I described above should work from Scheduler 3.3.0 on. Possibly you're using an older version - which is it?