HONG KONG—A pro-democracy politician was among the victims of a brutal attack during the 22nd weekend of protests in Hong Kong, as the city becomes increasingly mired in a cycle of violence.

An unidentified man—who local media reported had gone on a stabbing spree—grabbed District Councilor Andrew Chiu by the neck and shoulders, biting a part of his left ear off. A crowd of onlookers cornered and attacked the man before police arrived. Mr. Chiu is the latest in a string of pro-democracy figures to be attacked in Hong Kong.

In another district, pro-democracy protesters smashed a ticketing counter inside a subway station, and were chased by riot police into a bustling shopping mall. Protesters and mall-goers flashed laser beams at armed officials in response.

The violence Sunday followed demonstrations a day earlier in which tens of thousands of people took to the streets, while police fired tear gas and water cannons in an effort to disperse the crowds.

“Hong Kong seems to be trapped in a weekly cycle of unrest and repression, conflict between protesters and authorities, with no clear endgame on either side,” said Antony Dapiran, a lawyer and the author of a forthcoming book on the protests. “The protesters are not giving up as the government had hoped, while the government is taking no action at all to resolve the crisis.”

The monthslong movement was sparked by an extradition bill that would have allowed people in this semiautonomous Chinese city to be tried in mainland China’s more opaque legal system. The government withdrew the bill last month, as demonstrations became more violent, though the movement has snowballed into a call for greater democracy and freedoms.

Those demands include a direct election for the city’s leader—currently selected by a pro-Beijing election committee—amnesty for arrested demonstrators and an independent inquiry into alleged police misconduct against protesters.

Hong Kong Chief Executive Carrie Lam softened her tone on a police inquiry last month, saying she would consider it after assessing the results of a continuing probe by an independent police complaints’ committee.

Mrs. Lam is scheduled to meet Chinese Vice Premier Han Zheng in Beijing on Wednesday. The visit comes after the central government in Beijing said it planned to ramp up efforts to integrate Hong Kong with the mainland by strengthening patriotic education and overhauling how the city’s leader and other top officials are appointed and removed.

An attempt to introduce national education into Hong Kong schools in 2012 was withdrawn after it sparked protests by students.

“This is how China plans to brainwash the next generation of Hong Kongers,” said 62-year-old Allan Fong, a retired airport worker who came out to protest Saturday at a large public park. “Whether they appoint Carrie Lam or another leader—they are all the same to us, puppets in the hands of China,” he said.

A boy places a paper crane on the floor at a shopping mall in Hong Kong. Photo: kim kyung-hoon/Reuters

As thousands swarmed the park on Saturday, police fired multiple volleys of tear gas in an attempt to disperse the illegal—but largely peaceful—gathering. Later, police chased protesters along major thoroughfares, spraying them with blue-dyed water.

“I feel that as long as these cases keep appearing, Hong Kong people will just get more angry, and it may even push the peaceful protesters to become more violent,” said Sherry, a 14-year-old protester.

While protesters have dwindled in numbers since the movement was at its peak in June, the momentum shows no sign of waning in this global financial hub. The unrest is also taking an economic toll. Quarterly figures last week showed Hong Kong had plunged into recession for the first time since the 2008 financial crisis.

“People are finding ways and reflecting what will be next,” said Eric Lai, the vice-convener of the Civil Human Rights Front, which organized a march attended by more than 1.7 million people in June. While some protesters have taken a more radical turn, others have formed human chains, created so-called Lennon Walls and sung in shopping malls.

Overall, Mr. Lai said, he doesn’t see people giving up.

—Natasha Khan contributed to this article.

Write to Preetika Rana at preetika.rana@wsj.com

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