Bristol City Council has agreed to make £28m of savings - about 7% of its budget - in the next financial year.
Tuesday's meeting was beset by delays after a member of the public was arrested and some councillors walked out.
About 340 posts will go and council tax will be frozen, it was decided.
The Liberal Democrat-led authority said "finding efficiencies, reducing overheads and cutting management costs" amounted to more than 80% of savings.
A council spokesman said about 180 posts were likely to go through vacancies, redeployment and natural wastage.
He said 160 staff would potentially face redundancy.
Alan Brown, from the Easton area of Bristol, was one of about 12 people who were ejected from the meeting by police and council security for repeatedly shouting out.
He said he is not a member of a political party, but supports the Bristol and District Anti-Cuts Alliance.
He said: "Democracy from the Greek demos, rule of the people, we are the people. What we are doing is democracy in its strictest sense.
"The council are supposed to work for us."
Barbara Janke, leader of the council, said the situation was "unprecedented" due to central government funding cuts.
"This budget protects as far as possible the frontline services to the most vulnerable while supporting the enormous strengths of our city and its economy," she said.
"It also freezes council tax, recognising the pressure on hard-pressed families.
"We do feel that cities have been unfairly hit and we continue to lobby government at every opportunity, making the case for cities and their importance as the economic dynamos of the country."
Police were called when protesters disrupted the council meeting on Tuesday.
The public gallery was cleared after repeated interruptions, and Labour councillors walked out in protest at the public being told to leave.
Helen Holland, leader of the Labour group, said: "We voted against the whole budget, and none of our amendments - which would have mitigated some of the worst effects of the Lib Dems' proposals - went through as they were all voted down by the Lib Dems."
Police said they had arrested one person for breach of the peace during the debate.
The council's plans to cut 340 jobs during the next financial year saw a number of protests leading up to the setting of the budget.