Delete only referenced Nodes
This could be solved by creating a simple view with VBO. Try this steps:


Create a view of content, without any filter criteria.
Add a relationship to the view of the reference field in the 'student' content type. Say 'field_invoice'.
Add a filter to the view of "content type", select 'invoice'. Use the relationship in the filter that was created in step 2.
Add a filter of "content title". Expose this filter. Use the relationship in this filter too.
Add a VBO field of type  "Bulk operations: Content (Content)". Select 'delete' from the operations.


From this view, you should be able to filter by name of any student. It will list the invoices. And using VBO, you should be able to delete them.