Council leader Barrie Grunewald has pledged to use all available powers to help drive up standards at Hope Academy.
Coun Grunewald spoke out after it emerged on Thursday the principal of the faltering academy, John Gannon, and chair of governors, Prof Bart McGettrick, had resigned.
The school, set up after a merger between Newton High and St Aelred’s, was the subject of a critical Ofsted inspection last year.
The schools watchdog is expected to report next month that work to improve standards is not progressing quickly enough.
Coun Grunewald said the council will now work with the school authorities to implement changes.
He said: “Last year I announced my commitment to drive up school standards.
“We formed an Education Task Group ‘Every Child Matters’ to ensure that attainment levels across the borough would improve and that action would be taken where improvement is weak.
“I warned that schools that have coasted in the past would no longer have that option. I pledged that we would intervene in under-performing schools and other providers, including the use of formal powers available to the local authority.
“I am deeply concerned that the standards expected of the Hope Academy – which is independent of full council control - are not being achieved.
“There can be no tolerance of failure therefore along with the other organisations involved with the school – including Hope University and the
Archdiocese - we will be taking swift and appropriate action to get the academy back on track as quickly as possible.
“It has already been agreed that the Principal will step down and there will also be a change in the Chair of Governors.”
The local authority is also working with the sponsors to put in place interim school leadership in partnership with an outstanding school.
“Parents should be assured that collectively we will get this school back on track.