The men, 34 and 24, were inside 1147 Fulton St., near Franklin Avenue, about 5 a.m. when the suspect threatened them with a "cutting instrument" while making the derogatory remarks, police said.
The suspect, who can be seen in police footage released Tuesday, slashed the 34-year-old man across the face and then stabbed the younger man in the right side of his torso before slashing his right shoulder, police said.
The incident is being investigated as a hate crime, according to an NYPD spokesman.
The suspect is in his early 20s and about 150 pounds, police said.
Anyone with information should contact Crime Stoppers at (800) 577-TIPS (8477).