Cassidy grew up in Sydney, and attended the Our Lady of Mercy College in Parramatta, a suburb of Sydney. She began her medical studies at the University of Sydney and completed them at Oxford University in 1963. She wanted to become a plastic surgeon but couldn't keep up with the 90-hour week, so she went to practise medicine in Chile during the government of Salvador Allende.

In 1975, Cassidy was caught up in the violence of the Pinochet regime. She gave medical care to a political opponent of the new regime who was being sought by the police. As a result, she was herself arrested by the Chilean secret police, the DINA, and kept in custody without trial. During the early part of her custody, she was severely tortured in the notorious Villa Grimaldi near Santiago, Chile, in order to force her to disclose information about her patient and her other contacts.

On her release from custody and return to the UK, Cassidy's description of her experiences, including her account of her torture on the parrilla and her imprisonment, did much to bring to the attention of the UK public the widespread human right abuses that were occurring at the time in Chile. Her story appeared in news media and in her book, Audacity to Believe..

After a period of recovery from the physical and psychological effects of her ordeal (during which she briefly became a nun), Cassidy continued to practise medicine in the UK. In 1982, she became Medical Director of the new St Luke's Hospice in Plymouth, a position which she held for 15 years. She then went on to set up a palliative care service for the Plymouth hospitals.

Cassidy, a Roman Catholic, has written a number of books on Christian subjects and has been involved with a number of charitable organisations such as patronage of The Prison Phoenix Trust.