Officers were called to Worksop Road, Budby, at around 12.30pm on Thursday, August 8 following reports of the knife incident.
A 83-year-old woman has been taken to hospital for treatment for injuries that are currently believed to be life-threatening.
The man has been taken to hospital for treatment of injuries believed to be minor.
The incident is contained and officers are not looking for anyone else in connection with the incident at this time.