How to remove Student by Application from Student Group on a certain date automatically?

Students sometimes end Programs and Leave groups.
They are write applications and I need remove student from group on a certain date!
I need create Student Remove Application (or something like that) and remove him automatically when the date will come.

How to realize this?
How can I create document, like Student Leave Application for example?

Where should I start? What document or code should I create? Or maybe I can do it without programming?