She was born in Kingstown (now Dún Laoghaire) in County Dublin, and raised in Dungarvan, County Waterford. She was one of the numerous children of Benjamin Purser, a prosperous flour miller and brewer, and his wife Anne Mallet. She was related to Sir Frederic W. Burton, RHA (1816-1900), who had married Hannah Mallet. The Purser family had come to Ireland from Gloucestershire in the eighteenth century. Two of her brothers, John and Louis, became professors at Trinity College Dublin.
Until her death she lived for many years in Mespil House, a Georgian mansion with beautiful plaster ceilings on Mespil Road, on the banks of the Grand Canal. Here she was "at home" every Tuesday afternoon to Dublin's writers and artists; her afternoon parties were a fixture of Dublin literary life.  Mespil House was demolished after she died and developed into apartments. She was buried in Mount Jerome Cemetery beside her brothers John and Louis.
At thirteen she attended the Moravian school, Institution Evangélique de Montmirail, Switzerland where she learnt to speak fluent French and began painting. In 1873 her father's business failed and she decided to become a full-time painter. She attended classes at the Dublin Metropolitan School of Art. She joined the Dublin Sketching Club, where she was later appointed an honorary member. In 1874 she distinguished herself in the National Competition. In 1878 she again contributed to the RHA, and for the next fifty years became a regular exhibitor, mainly portraits, and showed an average of three works per show.
Sarah Purser became wealthy through astute investments, particularly in Guinness, for which several of her male relatives had worked over the years. She was very active in the art world in Dublin and was involved in the setting up of the Hugh Lane Municipal Gallery, persuading the Irish government to provide Charlemont House to house the gallery.
She was the second female to sit on the Board of Governors and Guardians, National Gallery of Ireland, 1914-1943.
She was made an Honorary Member of the Royal Hibernian Academy in 1890; first woman Associate Member in 1923 and the first woman Member in 1924.
In 1924 she initiated the movement for the launching of the Friends of the National Collection of Ireland.
Archives relating to Sarah Purser are housed in the Centre for the Study of Irish Art, National Gallery of Ireland.
When the Viceroy of Ireland commissioned her to portray his children in 1888 his choice reflected her position as the country's foremost portraitist.
In 1977 Bruce Arnold noted
Various portraits painted by Purser are held in the National Gallery of Ireland.
Sarah Purser financed An Túr Gloine (The Tower of Glass), a stained glass cooperative, at 24 Upper Pembroke and ran it from its inauguration in 1903 until her retirement in 1940. Michael Healy (1873-1941) was the first of a number of distinguished recruit, such as Catherine O'Brien (1882-1963), Evie Hone (1894-1955), Wilhelmina Geddes (1887-1955), Beatrice Elvery (1881-1970) and Ethel Rhind (c.1879 -1952). Purser was determined the stained glass workshop should adhere to true Arts and Crafts philosophy: 'Each window is the work of one artist who makes the sketch and cartoon and selects and paints every morsel of glass him or herself'.
Purser did not produce many items of stained glass herself. Most of the stained glass works were painted by other members of the co-operative, presumably under her direction. Two early works, 1904, were St. Ita for St. Brendan's Cathedral, Loughrea and The Good Shepard for St. Columba's College, Dublin. Her last stained glass work is thought to be The Good Shepard and the Good Samaritan, 1926, for the Church of Ireland at Killucan, Co. Westmeath.
An Túr Gloine archive is held in the Centre for the Study of Irish Art, National Gallery of Ireland.