How do you Abolish a Cabinet Department?

[True Federalist (진정한 연방 주의자)]

It takes an Act of Congress to create or abolish a department or agency, or to transfer responsibility from one department to another.  Note that from time to time Congress had granted the President authority to enact reorganization plans to move or consolidate functions from one agency to another, but it has been decades since the Congress has let the President do so.  Mainly that is because of INS v. Chadha which in 1983 found the legislative veto to be unconstitutional, and the reorganization authority which had been granted made use of it.  Congress has generally been unwilling to give the executive branch carte blache to reorganize itself.

[True Federalist (진정한 연방 주의자)]

Acts of Congress suffice, but it's not possible to entirely get rid of the Cabinet if for some stupid reason anybody would want to, since the 25th Amendment assumes its existence.

Not really.  First off the 25th doesn't call it the Cabinet, and second of all what it does say is:

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So for example, if the Congress wanted the Supreme Court or the Joint Chiefs of Staff to vet the Vice President's determination that the President is incapable of performing his duties, it could.

There is one weakness in the 25th.  What if there is no Vice President to trigger the inability section?  At that point, things revert back to the original Article II Section 1 Clause 6 muddle.