The driver, 44, was assaulted in Eastfield Avenue in Cambuslang, on the outskirts of Glasgow, on Friday night, suffering an injury to his neck.
He got out of the car and the suspect drove off. The vehicle was later found abandoned in Morar Drive.
Police said a 68-year-old woman was attacked in Dukes Road shortly after the incident, at around 7.50pm, and was injured in the chest. Both the driver and the woman are being treated at Hairmyres Hospital where their conditions are said to be serious but stable.
A 33-year-old man was taken to Glasgow Victoria Infirmary, where he was detained, in a stable condition.
Officers are not looking for anyone else in connection with the incident.