What is the meaning, and origin, of the phrase "breaking windows with guineas"?

Solution 1:

To add to what FumbleFingers says: the phrase was coined by politician Henry Fox during the seven years' war to ridicule William Pitt and the British government that was spending quite a lot of money for very little results against the French.
I have found an academic paper on the subject... it's in French.

I had never heard or read the phrase before. As to whether "cut off your nose to spite your face" really means the same I wonder. Couldn't we say "kill a fly with a sledgehammer"?

Solution 2:

During the Seven Years' War (1756-1763), Britain's ruinously expensive naval sorties against France were actually inflicting very little damage. In the specific case of the Sept 1757 Raid on Rochefort, British MP Henry Fox said it was like breaking their windows with guineas (i.e. - using and thus losing our most valuable coins as missiles, simply to break their glass windows).

It's really just a little-known quaint archaism. You're more likely to hear Cut off your nose to spite your face today.