They were arrested after police officers called to an incident in Carlisle Street, Attercliffe, found a 54-year-old man with a stab wound to his leg.
A vehicle was reported to have left the scene before they arrived.
Shortly afterwards, a 27-year-old seriously injured man turned up for treatment at Rotherham General Hospital.
Both men received medical attention and were later discharged.
Levi Farrier, 27, of Market Square, Goldthorpe, Barnsley, has been charged with wounding with intent.
Barrington Allen, 54, of Lowedges Crescent, Lowedges, Sheffield, has been charged with dangerous driving.
Both have been remanded in custody pending court cases.