It is a practice for ministers to convey their decisions to the department, and they do use different means. You can write “do not agree”, strike it across, as you said, “no, do not agree”, initial it, and date it.
It would not be, in my view, a good practice to just send a document back. Then it's not clear to the deputy what the decision of the minister actually was. My preference would be to have a written decision.