The woman, a resident of New Delhi, had gone to see the man in Sector 15 of Noida when the incident took place, a police official said.
The woman suffered injuries on her neck in the knife attack after which she was rushed to a nearby hospital from where doctors referred her to Delhi, the official from Sector 20 police station said.
The accused was absconding, the official said, adding probe was underway.
In another incident, two men were arrested in Sector 20 area for allegedly attacking a woman with stones and spitting on her, the police said.
The duo also spat on her, she added.
The accused have been arrested, the police said.