Tibetan Wild Asses are generally social animals and live in family groups. They sometimes gather together in large herds, which may number several hundred individuals. However, these herds are not permanent groupings, but temporary aggregations, consisting either of young males only, or of mothers and their foals. Older males are typically solitary and defend their territory from rivals, and dominate any local groups of females. Territorial males sometimes become aggressive towards intruders, kicking and biting at them, but more commonly chase them away after a threat display that involves flattening the ears and braying. Tibetan Wild Asses are diurnal and spend most of the day grazing; during the periods of dry seasons, they may gather in herds and travel great distances in search of food. Other than humans, Tibetan Wild Asses have only one real predator – the Himalayan wolf. They defend themselves by forming a circle, and with their heads down, kick out violently. As a result, wolves usually attack single animals that have strayed from the group. They are generally quiet, but when they feel threatened they will make a loud snort.

Tibetan Wild Asses breed between late July and late August; during this time, older males court reproductive females by trotting around them, and then chasing them prior to mating. After the gestation period of 7 to 12 months, females give birth to a single foal. Females are able to breed again almost immediately after birth, although births every other year are more common. Foals weigh up to 35 kg (77 lb) at birth and are able to walk within a few hours. They grow quickly and are weaned at one year of age.