No, snow leopards do not kill humans. In fact they rarely attack humans in the wild. There are only a few records of snow leopards attacking people and no records of this cat killing humans.
“They readily relinquish kills of domestic livestock even to a child brandishing a stick. They rarely defend themselves, and there are many records of snow leopards being beaten or stoned to death by otherwise unarmed villagers”.
It is a sad picture but it clearly indicates the non-aggressive attitude of this superb large wild cat towards humans.
They are known to become exceptionally tame and gentle in captivity. They can form close bonds with their caretakers we are told. Helen Freeman of the International Snow Leopard Trust (a great organization) tells the story of ‘an anonymous writer’.
“In captivity, it is far the tamest and gentlest of the large carnivora, not excepting the puma. Unlike the latter it is a sleepy, quiet animal, like a domestic cat.”
Please note that the anonymous writer adds that the puma is also relatively gentle. This characteristic is rarely understood by those who wish to shoot it for entertainment.
Source: Wild Cats of the World. Quote about the gentleness of this cat is from: The snow leopard today and yesterday. International pedigree book of snow leopards 4: 85-97 by H Freeman.