Professor Susan Deacon, a former Labour minister, says these are "fundamentally flawed in her resignation latter to Justice Secretary Humza Yousaf.
“There is little more I can do to make these arrangements work effectively," Prof Deacon states
She was appointed in 2017 with a view to bringing a "fresh perspective" to the role after a series of rows over the way the SPA operates.
She states that she has made "every effort" to make the current framework work "as I believe it was intended."
But Prof Deacon adds: "I would suggest that the Scottish Government thinks afresh about how the police service is scrutinised and held to account and how, or if, a better separation between politics and policing, and indeed between the police service and those who oversee it, can be achieved.
"I would be pleased to share my thoughts and reflections on these matters with you, and indeed with the Scottish Parliament’s Justice Committee, at any time."
Vice Chair David Crichton will now head up the SPA board until a new Chair is appointed, said:
He insisted Police Scotland now has a "strong, resilient leadership team in place" as a result of her contribution.
He added: "We believe that the system of governance and accountability for policing in Scotland that was envisaged by the founding legislation is a sound one and can work effectively. Members of the Authority are fully committed to taking forward the range of work required within the SPA and with other partners to do so.
“While we respect this personal decision of the Chair, our collective focus will be on working together with our dedicated staff team to build on recent progress, deliver the actions and improvements already identified, and redouble the SPA’s focus on the issues of greatest importance to policing and the public.”
Mr Yousaf said today there had been "significant improvements" across many areas of the police service during Prof Deacon's two years in the role.
He added that changes were being made to address "leadership, governance and accountability concerns" in a letter to Holyrood's justice committee convener Margaret Mitchell.
It dded: "The recent HMICS report made clear that there is a consensus from key post holders in the SPA, Police Scotland and other stakeholders that the 2012 Act establishes the right model of centralised governance of police by an independent police authority, and that the functions of the SPA are sound."
Mr Yousaf added that the SPA is also committed reviewing the "governance and accountability framework", in line with the recommendations of a recent HMICS thematic inspection report.
"I am encouraged that significant progress has been made and remain committed to this going forward."