No matter what you may have seen on TV, Van Gogh did not cut off his ear.
(Well not all of it anyway. He actually cut off the lower part of his left ear, leaving part of the upper ear still attached. He then wrapped the mutilated flesh in a piece of cloth and made his way to his favourite brothel where he presented it as a "present" to a prostitute. The police were called and Van Gogh was taken to hospital. The severed tissue was placed in a jar of alcohol in case it might be needed as evidence. Some months later it was thrown out. Nowadays they'd probably sell it on eBay.)
Source: Van Gogh: His Life and Art by David Sweetman