The suspect, described as a man in his 20s who is missing a tooth, struck first on a northbound 4 train at Bleecker Street, where he punched a 35-year-old man in the face just before 1:30 a.m. while clutching the box cutter in his fist, police said. He left a gash across the face of the victim, who got off at Union Square.
The suspect then fled the train at the Union Square stop, and when he came across a 20-year-old woman in the station, he slapped her in the face, police said.
As the suspect left the station, climbing the stairs near the Food Emporium at 10 Union Square East, he asked a 46-year-old man for $2, police said. When the man refused, the suspect slashed him on the right side of his face.
The suspect then crossed 14th Street near Fourth Avenue, demanded a dollar from a 59-year-old man who was waiting for the M14 bus and then cut the man's face, police said.
The three slashing victims were taken to Bellevue Hospital for treatment, according to police. All were in stable condition.
Police described the suspect as a heavyset man wearing a hat, a white hooded sweatshirt, black vest, blue jeans and red sneakers.
Anyone with information is asked to call the NYPD's Crime Stoppers Hotline at 800-577-TIPS. The public can also submit tips by logging onto the Crime Stoppers website or texting their tips to 274637(CRIMES), then entering TIP577.