Dylan Andrew Quick also cut at least 10 others, the women claim in a suit filed in a Houston court, Courthouse News Service reported Monday.
Marcela Catano and Xiomara Guerra claim the 21-year-old Quick attacked as students at Lone Star College returned from spring break in April.
The lawsuit claims Quick roamed the school's health science, randomly cutting students.
Catano said she was attacked as she descended a flight of stairs. A male student in front of her told her to run, and Quick then stabbed her and slashed her throat.
Guerra said Quick ran past her on the first floor, then turned around and stabbed her in the left hand and right cheek as she attempted to defend herself.
Both plaintiffs said they had permanent scars from the attacks, as well as emotional trauma. They are seeking medical expenses and punitive damages.
Police said Quick told them he had fantasized about cutting off people's faces since he was a child.
He asked to be put on suicide watch in jail after his arrest, court records indicated.