I'm not sure if "Cutting off your nose ..." [note cutting] is descended from "paying through the nose". This latter comes from the Danish habit of cutting off the noses of Ancient Britons (no Age Concern in those days!) who couldn't/wouldn't pay the Danegeld. Nowadays we have agents, of course.

Of course, a pedant would say that this isn't actually etymology. I woul;dn't say that, 'cos I can't remember what it should be called.

Steve