She was born in Bury, Lancashire on 23 February 1839 to Scottish parents, and went to a small Edinburgh boarding school in the 1850s. While staying with friends she met her husband Rudolph Crudelius, a German wool merchant, in Leith, and married him in 1861. He travelled a great deal on business and his wife wrote him frequent long letters, including discussion of ideas as well as personal matters. Later she would use her fluency as a correspondent to pursue her social and political causes.
In 1866 Mary Crudelius put her name to one of the earliest petitions to Parliament about votes for women. She went on to commit herself to the cause of education for women, starting in 1867 when she spoke out at a ladies' discussion group called the Edinburgh Essay Society. Not long afterwards some of these women, including Crudelius and Sarah Mair, set up the Edinburgh Ladies' Educational Association (ELEA) with the aim of ensuring equal educational opportunities for women.
Crudelius did not want a separate women's college but the admission of women to universities. Nevertheless she opposed the idea of co-educational classes and went to some trouble to arrange things so as not to attract criticism. Although Sophia Jex-Blake was campaigning during these years for women's medical education, the ELEA tried to stay distant. Crudelius was a respected leader in the group and helped steer the association through a few internal disputes and one dispute with the university about details of the plan to offer a university certificate to women passing examinations after attending ELEA lectures.
The association designed its classes according to the university's arts curriculum and to its standards, finding support from several eminent male professors, especially David Masson. 400 women went to Masson's first lecture on English Literature in 1868, with 250 of them staying for the whole series. The certificate was introduced successfully in 1872, though Crudelius hoped there would ultimately be full university degrees for women, but her health had been poor for some time and she did not live to see this happen.
She died on 24 July 1877, fifteen years before the first Scottish universities opened their doors to women undergraduates in 1892. Her two daughters were educated through the association in the 1880s and for a few years there was a Crudelius Hall of residence. This was replaced by the Masson Hall in 1897. A Memoir of Mrs. Crudelius was published in 1879 containing some of her letters, poems, and ELEA reports she had written.