Would New Zealand ever fire a coach?

Are we too polite to fire anyone - either at (pro) club level, or for the national team?

Too cheap to pay them out.

I wouldn't have thought so.  More likely to "force them to resign".

It's rare anywhere in the world for a coach/manager to get proper "fired" isn't it? 

Don't they usually come to a mutual agreement, or the coach/manager himself resigns?

I think they get fired, but for the sake of the releasing the information to the media they say it was mutual to save face.