Stuff is running this:
Does New Zealand need a process for removing impaired Prime Ministers?
They feature four earlier Prime Ministers – Savage, Kirk, Muldoon and Ward as being impaired.
I think my heading is more accurate.
Link to the full article follows.
I am backing my two as the first two who should have been removed from office. Incompetence and an Agenda to drive New Zealand into financial oblivion and racial division are the first two reasons we should look at when considering impaired Prime Ministers.
No Minister 
We do have a process. The Governor General can just sack them.
That and their fellow Cabinet Ministers who can see their own futures going down the tube with their leader and fix it with a simple vote, as people from Jack Marshall to Jim McLay to Bolger have found out.
The Labour Party is a bit more complex – IIRC it’s now an all-party-member vote unless it’s close to an election when the MP’s can step in? Perhaps that’s where Stuff is coming from with this?
It’s not the USA where it takes the 25th Amendment, and it’s so challenging that nobody has tried it.