Spence was born in Mel Rose, Scotland, as the fifth child in a family of eight. In 1839, following sudden financial difficulties, the family emigrated to South Australia. Arriving on 31 October 1839 (her 14th birthday), on the Palmyra, at a time when the colony had experienced several years of drought, the contrast to her native Scotland made her "inclined to go and cut my throat". Nevertheless, the family endured seven months "encampment", growing wheat on an eighty-acre (32 ha) selection before moving to Adelaide.
Around 1850, having become disillusioned with some doctrines of the Church of Scotland, she began attending the Adelaide Unitarian Christian Church in Wakefield Street. She preached her first sermons there in 1878, (though she was not the first woman to preach there, that honour going to Martha Turner of Melbourne, sister of Gyles Turner) and filled in for the pastor Dr John Crawford Woods during his absences 1884–90.
Her first work was the novel Clara Morison: A Tale of South Australia During the Gold Fever. It was initially rejected but her friend John Taylor, found a publisher in J W Parker and Son and it was published in 1854. She received forty pounds for it, but was charged ten pounds for abridging it to fit in the publisher's standard format. Her second novel Tender and True was published in 1856, and to her delight went through a second and third printing, though she never received a penny more than the initial twenty pounds. Then followed her third novel, published in Australia as Uphill Work and in England as Mr Hogarth's Will, published in 1861 and several more though some were unpublished in her lifetime including Gathered In (unpublished until 1977) and Hand fasted (unpublished until 1984).
In 1975 she was honoured on a postage stamp bearing her portrait issued by Australia Post.
Her image appears on the commemorative Centenary of Federation Australian five-dollar note issued in 2001.
Although Spence rejected both of the two proposals of marriage she received during her life, and never married, she had a keen interest in family life and marriage – as applied to other people. Both her life's work and her writing were devoted to raising the awareness of, and improving the lot of, women and children. She successively raised three families of orphaned children – the first being those of her friend Lucy Duval.