"Cutting off the nose to spite the face" we say when we want to describe a needlessly self-destructive reaction, somebody who is acting out of pique, or who is pursuing revenge in a way that would damage him/her more than the object of his/her resentment. In Italy there are many ways to describe this particular action because it is, unfortunately, a common and dangerous problem, but one expression among all describes it perfectly: cecami un occhio, literally poke one of my eyes out!
A starving farmer finds an old oil lamp in his field. He rubs it and a genie comes out. "I will grant you a wish," the genie says "but your worst enemy will get double of whatever you wish." The farmer can't make up his mind, walking back and forth, imagining different scenarios. He could wish for immense wealth or food to last him a lifetime since he is starving, but his hatred for his enemy is such that he turns to the genie and says: "Poke one of my eyes out".
It sounds like a joke, right? Now apply it to politics, business, family, emotions, and it will turn into what it really is, the description of a sad, bitter human trait.