The city principals’ union is blasting Chancellor Richard Carranza’s “failed leadership” for inking a new last-minute agreement to let many more teachers work from home.

But it means that principals will now have to redo their schools’ schedules yet again — days before in-person classes for students in K to 12 are set to begin next week.

“It causes more revisions at the 11th hour,” a Brooklyn principal told The Post. “This is a programming clusterf–k.”

Under the last-minute deal, supervisors may require teachers to remain on-site “on an as needed basis only.”

The DOE has already granted 16,025 teachers — 21% of the citywide total — coronavirus medical exemptions that will allow them to work from home.

Previously, any teacher without an exemption was required to be in school each day — even when teaching remote classes to kids learning from home. The policy has been challenged in court.

But the United Federation of Teachers argued against the rule, and finally won the concession.

The Council of Supervisors and Administrators, which represents principals, issued a blistering statement on Saturday, complaining they were left out of the loop.

“The Chancellor and his team have once again demonstrated a complete lack of respect for school leaders as we still wait for the DOE to release information regarding the new memorandum they signed just before close of business yesterday, an agreement the press have already reported on,” the CSA said.

“It astounds us that they seemingly had no plans to notify and debrief principals, who must now somehow find a way to implement their new agreement, before it was distributed widely.”

The statement concludes: “CSA will now be calling for an emergency executive board meeting, and we will share more on our public response to the DOE’s failed leadership as soon as we are able.”

David Bloomfield a Brooklyn College and CUNY grad center education professor, said the CSA statement conveys a crisis:

“Principals are now in open revolt, teachers confused, and parents at wits end over the constant policy shifts that make attention to learning almost impossible,” he told The Post. “Poor planning, a mayor and chancellor disconnected from the field, and flawed messaging make unsubstantiated rumors of Carranza’s resignation and all-remote instruction for grades 6-12 sound more and more plausible — and maybe a relief.”

City Councilman Mark Treyger, education committee chair, tweeted a text he received from a principal: “I can’t do this anymore. I’m not OK. I can’t look my community in the eye and tell them with a straight face that we’re OK. I want to quit.”

Also Saturday, a “heartbroken” Gina Battista, the principal of Tottenville HS on Staten Island sent a letter to families announcing her decision to start the new year all remotely — giving up on Mayor de Blasio’s plan to give in-school instruction to students one to three days a week.

“Tottenville HS would need an excess of additional teachers that is just not presently available,” Battista wrote. However, all students will get live instruction online, she added.

DOE spokeswoman Danielle Filson said in a statement, “Collaboration is a key part of reopening and we meet weekly with our partners in labor to discuss upcoming policies and guidance. We are making decisions as the pandemic evolves that are in the best interest of our students, families, teachers and staff.”

Another source familiar with the negotiations said CSA leadership was aware of the negotiations for months and received a draft of the agreement several days ago, but a CSA rep denied it.