Nottingham City Council budget plans, which were approved for the current year, included 550 job losses, a council tax rise of 5%, and cuts to youth services.
Nottingham City Council, which is controlled by the Labour Party, will soon publish its budget for the financial year beginning April 2025.
The authority, which declared effective bankruptcy towards the end of 2023, is facing a £69m shortfall, rising to a cumulative £172m over the next three years.
In her resignation letter, Quddoos said: "The budget for 2025 is being written. It is likely that the cuts in it will be just as damaging as the cuts made in 2024, if not more so.
"The people who will be most impacted by these cuts are going completely unheard.
"If I cannot speak up for them in the way they want me to without being sanctioned for it, I cannot remain in the party."
Quddoos will continue to represent her Berridge ward as an independent councillor.
It is understood an investigation by Labour into Quddoos had not concluded when she resigned.
A Labour Party spokesperson said: "The new Labour leadership at Nottingham City Council is focused on taking the tough and responsible decisions to fix our local authority, and it is making progress.
"We will continue to focus on this work as a team and get on with the task at hand for the people of our city, not be distracted by sniping from the sidelines."