The Qing Dynasty mandated that all Han Chinese wear the queue as a sign of obedience to the dynasty. Failure to do so indicated that the person was likely a dissident and those who were caught without one were considered rebels and were executed for treason. Therefore, the act of cutting the queue was a sign that you were essentially forever severing yourself from China, for to return to China without your queue could literally be a death sentence. That being said, like many other Chinese government policies, there was no strict punishment or legal standard, so some people who cut their queues may have simply been dismissed from civil service and the like.

Historically, there were several Chinese who, having immigrated to America, cut off their queues entirely. But by the 1870s and especially after the First Sino-Japanese war in the 1890s, the queue was already being abandoned by the Han Chinese. Sun Yat-Sen, one of the later founders of Republican China, cut off his hair in anger at the Qing's incompetence in their military defeat to Japan. Severing the queue soon became a sign of rebellion and Chinese nationalism, and in one of several conciliatory moves the Qing government ended the queue mandate in 1910. This did little to deter Chinese revolutionaries, however, whereupon the Qing Dynasty ended during the Xinhai revolution.

Relevant scene. Hair cutting is at around 9:40. Clip contains violence, nudity, and racist terminology.