At a full council meeting, members voted by a margin of 49 to 6 in favour of a motion urging Mr Winter to quit and accept responsibility for "the failure of the children's service".
Four councillors abstained.
The vote was triggered by the Department for Children, Families and Schools' decision to order an inquiry into Doncaster Metropolitan Borough Council’s children’s department.
The investigation follows the deaths of seven children in the local authority.
In addition, serious case reviews set up into the deaths involving neglect and abuse.
Last July, the mayor remained in office despite losing a vote of no confidence in the full council.