No, Leonardo da Vinci did not cut off his ear. This is a common misconception that often gets confused with another famous artist, Vincent van Gogh. Van Gogh is the artist who famously cut off a part of his own ear during a period of mental distress.
Leonardo da Vinci, on the other hand, was a Renaissance polymath known for his works like the Mona Lisa and The Last Supper. There are no historical records or evidence suggesting that da Vinci ever harmed himself in such a manner. His life was marked by his incredible contributions to art, science, and various other fields, but self-mutilation was not part of his story.