A man in New York City attacked four underage girls, at least some of them relatives, cops say ... and, video shows officers carrying the alleged attacker out of the building.

Watch the clip ... the man is being carried by multiple officers -- face down toward the ground, arms held behind his back before they put him on a gurney.

He's then tied down ... and, carted off by officers, his body tilted at a weird angle -- but still alive, though we're told he's in critical condition at the hospital.

According to the NYPD ... they received a call from an 11-year-old girl in Brooklyn this morning telling the dispatcher that her uncle had stabbed her and her siblings.

Officers rushed to the residence ... running into the building where they say they heard screams from behind one of the doors.

After smashing open the door to the apartment, New York City Police Commissioner Jessica Tisch says, the officers found a man holding a meat cleaver dripping with blood ... and, the walls and floors of the home were covered in blood as well.

Officers instructed the man to put down the knife several times, Commissioner Tisch says ... but, he allegedly refused and advanced on them -- which is when they shot him "ending the threat."

The NYPD has released pictures of the cleaver stained with blood ... as well a large kitchen knife also covered with blood. It's unclear who wielded this second knife.

The New York Post obtained pictures in the aftermath of the attack ... including one of a person -- presumably a victim of the attack -- covered basically head to toe in blood, though still standing on their feet.

Officers say four girls -- aged 16, 13, 11 and 8 -- were all rushed to a local hospital for treatment ... but, as of now, they are alive and expected to recover. It's unclear how exactly they are related to the man who cops say wielded the knife.