Renshaw, the pioneer of forensic pathology, was born in Rochdale in 1885, the son of a dentist. He qualified in dentistry at the University of Manchester in 1909, and in medicine in 1910. Renshaw worked as a pathologist at various Manchester Hospitals, including Christie, Manchester and Salford Hospital for Skin Diseases, Ancoats Hospital and the Royal Eye Hospital. He was later a director of the laboratory of applied pathology and preventive medicine, Manchester. Renshaw did research into bacterial causes of disturbed metabolism, and the use of chemotherapy in treatment of diabetes and cancer. He also developed artherepsin for the treatment of arthritic conditions.
There is no known family connection between Arnold Renshaw and the Renshaw family of Sale and Ashton-on-Mersey.