The obvious way to stop a bike lane is to vote against it. An example is University when the opposition to Mayor Miller passed an amendment to remove University from the bike lane plan that year.
The most egregious way to stop a bike lane, for which Toronto has become world famous, is to rip out existing ones. Thanks to spiteful Mayor Ford, Councillor Minnan-Wong and Councillor Berardinetti we are now three bike lanes fewer.
Those are the methods that get the most public attention. But even before a bike lane reaches a vote or is built, a bike lane can be stopped. John Street is a favoured north-south route for cyclists. Councillor Vaughan led a drive to turn it into a "pedestrian priority zone" (as well as a patio zone from what I can tell of the plans). The environmental assessment, which ended last year, resulted in a solution with no bike lanes. It didn't help to build trust in the process when the consultants largely ignored cyclists in the official count. Dave Meslin revealed the fudge of their recorded flatlined 2% bike mode share by conducting his own count (along with some help from yours truly and other volunteers) showing a much higher number during peak hours.
According to the EA, however, the bike mode share didn't matter since they were directed to create a pedestrian priority zone (which also happened to include motor vehicles, large and small). As a palliative, Vaughan had pointed out that Peter would become the alternative route, though we've yet to see much movement among staff or councillor to create that solution. Thus I'll hazard to say that the entire process was configured so that bike lanes would be excluded and never come to a vote.
Another way to stop a bike lane is to build local opposition. The current Vaughan says he supports separated bike lanes, but the older Vaughan actually blasted them as "barricaded". That doesn't sound like someone who supported separated bike lanes, but instead like someone who's trying to build local opposition to them.
Yet another way to stop a bike lane is to call for more community consultation or to make it a pilot project. Councillor Wong-Tam took these tactics with the Sherbourne protected bike lanes. The City's Cycling Unit staff went door to door along Sherbourne, consulted with businesses and residents groups, and held public consultation meetings for Sherbourne (where the majority of attendees supported the lanes). I was told by a staffperson at the time that Councillor Wong-Tam provided next to no help in making her constituents aware of the project. It all suggested an attempt at stopping the bike lanes by studying it to death.
It's easy to point out the idiocy of politicians who rip out bike lanes, but it's good to keep in mind that there are more subtle ways out there to kill a bike lane while trying to keep the "progressive" label.