She was born Sarah Theresa Dunne on July 2, 1846, in Akron, Ohio, to Irish immigrants John and Ellen Dunne, and was their fifth child. (Her eldest brother was Judge Edmund Dunne.) An accidental poisoning as a child left her with asthma and various health issues. In 1856, her family moved to California as part of the gold rush. She and her older sister, Mary, were left behind as students at an Ursuline boarding school. She entered the Ursuline convent in Toledo, Ohio, in 1861. Dunne took vows as an Ursuline on August 23, 1864. She was elected superior of her convent in 1872.

She left Toledo with five other Urusline nuns in 1881 and traveled to the Montana Territory in the United States to help establish missionary schools (parochial schools which also sponsored missionary work) for Native American tribes. She established a school and Ursuline convent in Miles City, Montana, in 1881, and then St. Labre's Mission School in Ashland, Montana, in January 1884. She established a girls' mission school at the already-extant St. Peter's Mission near Cascade, Montana, in October 1884. She nearly died of pneumonia there in 1885, but recovered after an African American ex-slave and friend of the family, Mary "Stagecoach Mary" Fields, traveled from Ohio to Montana to nurse her back to health.

A strong advocate for the unification of Ursuline chapters, she helped co-found the Ursuline Union in Rome, Italy, in 1900. At that time, Ursulines in North America were organized into a North Province and a South Province. Mother Amadeus was named Provincial Superior over the North Province. She was seriously injured in a railroad accident in 1902, which left her with a permanent limp. In 1905, she assisted three Ursuline nuns in founding an Ursuline presence in Alaska. She was named Provincial Superior over Alaska in 1910.

Mother Amadeus died in Alaska in on November 10, 1919. Her body was returned to Montana, and she was buried at St. Ignatious Mission.