The city’s embattled Thrive­NYC mental-health program missed a hearing on how to combat cop suicides amid a dramatic rise this year — because its director was on vacation.

“I anticipated asking Thrive some questions. I just didn’t think the toughest would be are you here?” City Councilman Joe Borelli (R-SI) said ­after the Public Safety Committee hearing Tuesday.

Borelli claimed Thrive was invited to the Tuesday hearing but did not show — while City Hall claims the program championed by First Lady Chirlane McCray never got an invite.

Upon learning of the hearing, Thrive director Susan Herman asked that the council hold off until after she got back from vacation, the mayor’s reps said.

The committee, helmed by Councilman Donovan Richards, could not find a date that worked, according a council spokesman. Thrive never sent a proxy.

First Lady Chirlane McCray’s $1 billion program came under fire last month after it pulled out of a mental-health seminar because a pro-cop group was signed on to sponsor the event. The mayor’s office, however, claims that ThriveNYC never canceled on the event.