The legal profession had previously expressed concern the scheme could threaten the fundamental principle that an accused person is innocent until their guilt is proven beyond reasonable doubt.
In a social media post, the SSBA described the pilot scheme as a “dangerous proposal”.
It stated: “Our opposition was a principled campaign based on a simple premise: either all of us matter or none of us matter. Once you start taking away some people’s rights, it never ends there.”
Roddy Dunlop KC, dean of the Faculty of Advocates, also said he was “very pleased” to hear the plan was being dropped.
John Mulholland, the convener of the Law Society’s public policy committee, said it was “unfortunate” that the decision had taken such a long time to be reached, and that the group had been “deeply concerned” about it.
The legislation also contained proposals to reduce the size of Scottish juries from 15 to 12 with a majority of 8 required for a guilty verdict.
Prosecutors from the Crown Office told the criminal justice committee that could make it harder to get convictions.
It is believed the government is now planning to keep juries at 15, but raise the requirement for a guilty verdict to a majority of 10.
That would be presented as a counter balance to the abolition of not proven and recent changes on the rules on corroboration.
Ms Brindley said Rape Crisis Scotland was “extremely concerned” about this step, as it would make rape convictions even harder to achieve.