Alexander Shand was born on 15 November 1840, at Petone, New Zealand, to Archibald Watson Shand and his wife, Elizabeth Alexandrina Greig Kilpatrick, who were among the first group of New Zealand Company immigrants. They were allotted land at Waiwhetu for their £100 subscription to the New Zealand Company's emigration scheme, and they expected to become landed proprietors in the new colony. When their pioneer labours were overwhelmed by economic troubles and war in the Hutt Valley, Archibald joined the customs service and the family moved to Wellington. Alexander's early education depended on the local school teachers, Church of Scotland ministers and his parents: his father was the son of the parish schoolmaster at Tain, Ross-shire, in Scotland, and his mother was described as well educated.
Archibald Shand was appointed sub-collector of customs and deputy postmaster in Otago in 1850; the family lived at Otakou. In 1855 he became resident magistrate and collector of customs on the Chatham Islands. He found it difficult to assert European authority over the Maori residents and to prevent their ill-treatment of the Moriori, enslaved after the 1835 invasion by Ngati Mutunga and Ngati Tama. In 1863 he was replaced by Captain William Thomas. Shand and his family became permanent farming settlers at Te Wakaru, supported by a pension negotiated through Robert Hart, their family solicitor in Wellington.
Alexander Shand remained on the family farm until 1870, when he and his brother-in-law, F. A. D. Cox, leased the Whangamarino block near Waitangi. As well as farming, Shand acted as clerk to the resident magistrate and as a licensed Maori interpreter; in this capacity he served judges and magistrates. He frequently appeared at Native Land Court sittings at Waitangi on behalf of Maori and Moriori witnesses unable to represent themselves. The isolation of his farming life and his lack of family – he never married – left Shand free to devote his spare time to studying the Moriori. His chief informant in this was Hirawanu Tapu, and his interest may have been stimulated by his contact with Percy Smith, who had gone to the islands as a surveyor in 1868.
The collaboration with Tapu was fruitful: Tapu collected information on Moriori traditions and history from living authorities in the Chatham Islands, and returned for further information if the material suggested questions to Shand. The material collected was published in the Journal of the Polynesian Society between 1892 and 1898; it appeared in 1911 as a book entitled The Moriori people of the Chatham Islands: their history and traditions. The book also dealt with the Jean Bart incident of 1838, dendroglyphs (tree-carvings), geography, and Moriori stone implements.
Alexander Shand died in a fire at his house on 28 July 1910. It was rumoured by some that the fire was deliberately lit to prevent his giving unfavourable evidence on a land claim, and even that he may have been pushed back into the blaze as he tried to escape: no evidence in support of either assertion has ever been produced. The fire was also believed to have destroyed his partially completed Moriori vocabulary, although the Reverend H. W. Williams probably used this in 1919.
Shand's death, and that of Hirawanu Tapu in 1900, meant that the Chatham Islands had lost 'the sole repositories of the knowledge of a lost race'. His valuable collection of authentic information on the Moriori was acknowledged by his contemporaries, one of whom wrote that 'Mr. Shand…is perhaps the only living authority on the language and traditions of [the islands'] now nearly extinct inhabitants'. Sir Robert Stout found time to call on Shand while the latter was under treatment for his arthritis at Rotorua thermal springs, and the headstone over Shand's grave at Waitangi stands engraved with an appreciation from the Moriori people. Perhaps more valuable was his assertion – largely overlooked until recently – that the Moriori were not a pre-Polynesian people who had been driven to the Chatham Islands by the invading Maori, but were themselves a Polynesian race who had settled the islands long before the Maori reached New Zealand. Now that this conclusion has been vindicated by research, Shand's place as a New Zealand ethnographer seems secure.