Hancock was born a Quaker in New Jersey. She began her Civil War nursing career inauspiciously when she arrived with other women volunteers in Philadelphia, Pennsylvania, in July 1863, shortly after the Battle of Gettysburg. At the time, the army was looking for older women to be nurses, and, at 23, Hancock was judged to be too young. She was the only one of the group not to be accepted as a volunteer nurse. Nonetheless, she found her way to Gettysburg, Pennsylvania, and began what became a well known and respected service as a nurse in the field.
After the war, she opened a school for African Americans in South Carolina. In Philadelphia, she founded several charity organizations and remained active in social work until her death.
Her popular collection of wartime letters is still in print.