Saunders was born on October 14 1865 in Brighton, England. She was educated first at Handsworth Ladies' College and in 1884 she entered the female-only Newnham College, Cambridge. There, she attended both Part I (in 1887) and II (in 1888) of the Natural Sciences Tripos.
She continued her post-graduate research, and served as a demonstrator at the Balfour Biological Laboratory for Women between 1888-1890 (where students from Newnham and Girton colleges received preparation for the Natural Sciences Tripos). She was the last director of that Laboratory between 1890-1914. She was also director of studies at Girton College (1904–1914) and Newnham College (1918–1925).
She was appointed a fellow of the Royal Horticulture Society from which she received the Banksian Medal in 1906. In 1905 she was one of the first women elected a fellow of the Linnean Society of London.
In 1920 she was the president of the botanical section of the British Association for the Advancement of Science. She also served as president of the Genetical Society, between 1936 and 1938.