The incident took place around 9.45am on Thursday when the 18-year-old victim was in her house in Ghodbunder Road locality with the accused Suresh Ramdas Wadekar and her mother, an official said.
The accused wanted the victim to accompany him to his house and stay there.
But the victim was reluctant and said she would accompany him once it stopped raining, he said.
The accused got annoyed and took a big knife from the kitchen and attacked the victim, and the latter’s mother when she tried to intervene, the official said.
The mother and daughter were rushed to a local hospital, where they are undergoing treatment, he said.
A case under section 326 (Voluntarily causing grievous hurt by dangerous weapons or means) against the accused, who also sustained injuries, he added.