The expression "cut yourself on the nose" is used in those cases when they want the interlocutor to remember something for a long time. And the outstanding part of the face has nothing to do with it.
Commemorative plaque
In ancient times, peasants did not know either a letter or an account. And if one asked the other for a loan of several bags of grain or flour, they could not make notes or draw up receipts. And so that there would be no disputes in the calculation, the one who borrowed brought with him a long wooden plaque called the “nose”.
On this plank, transverse notches were made according to the number of borrowed bags, then the plank was split from top to bottom, and each left half with nicks. When the debtor came to return the bags, both parties to the transaction folded their halves of the nose together. If the notches coincided, and the number of bags was equal to the number of notches, this meant that not one of the peasants had forgotten or mixed up anything.
The same custom existed in medieval Europe. In the Czech Republic, for example, in the 15-16 centuries. innkeepers widely used special sticks - "cuts" on which they applied, "cut down" with a knife marks on the amount of drinks drunk or eaten by visitors.
Homonymy
The word "nose" in the expression "chop yourself on your nose" does not mean the organ of smell. Oddly enough, it means "commemorative plaque", "tag for notes." The name of the tablet itself obviously comes from the old Slavic verb "carry" - so that there would be prok from nicks, this tablet always had to be carried with it. And when it is advisable not to forget or confuse anything, and they say: "Cut it on your nose!".
In addition, the word "nose" was used earlier in the meaning of offerings, bribes, and if someone could not agree with the person to whom this nose was intended, this unfortunate someone, as you might guess, remained with that very nose.
Thus, the phraseology “cut your own nose” lives to this day, and its original meaning has lost its meaning.