A tugboat worker was rescued by the NYPD Harbor Unit on Thursday night after part of his arm was severed by one of the boat’s ropes, police said.

The 27-year-old man was on a tugboat about a half-mile south of the Statue of Liberty at about 9 p.m., when his arm got caught in the line that was helping to move another vessel, cops said.

The line sliced through his left arm just below the elbow, police said.

The severed portion fell into the water and has not been found, they said.

Three officers in the NYPD Harbor Unit responded and quickly applied a tourniquet to the man, police said.

They then got the victim to Brooklyn Army Terminal, where he was taken to NYU Lutheran Medical Center, police said. He was conscious and alert, police said.