Strike action started at 06:00 BST on Friday, with the GMB union stating the majority of its members voted in favour of industrial action.
Employer Veolia said it was disappointed with the move.
The company, which runs waste management for Sheffield City Council, added it had been "working closely" with the union and its employees.
The GMB union, which represents 95% of about 180 workers, said about 92% of its members voted for action.
Peter Davies, from the union, said the dispute centred around what he called the "aggressive" use of disciplinary procedures and said there had been 96 gross misconduct cases in the last 12 months.
He said talks had taken place but a deal to rewrite disciplinary rules had not been agreed.
A spokesman for Veolia said extra crews will be working on Saturday and Sunday to complete any missed collections.
He added: "We are working hard to resolve this matter and to minimise the impact on bin collections for Sheffield residents.
"We have made significant progress towards resolving the current dispute, and we hope to conclude an agreement between ourselves and the GMB next week."
Refuse collectors have walked out in Sheffield in a 24-hour strike blamed on "aggressive" management practices.