Yes, a despicable act, but, should the minister resign? If he gave the instructions that led directly to the action, yes. If a minion, seeking for his own advancement, used "initiative" as a replacement for good sense, no, let the fallout fall on his career. A minister walks away from a problem, he has a good time for a few weeks, then gets another post after the next ministerial fowl-up while some other ignorant windbag gets to polish the ministerial chair with his trouser seat. Make the swine stay put and sort the problem, preferably without pay until the problem is seen to be sorted. Its called incentivisation, and sorting the mess in your own time, something that used to be common enough in real industry.
When a minister resigns, he doesn't have to make his way to the job centre like anybody in the real world, he doesn't have to seek re-election, he just hangs on, in the manner of a persistent dangleberry.
In the words of Ken Dodd, "By Jove, that feels better now!"