Born in I834 in Pictou, Nova Scotia, Alexander McLellan Mackay had a brief teaching career before becoming a telegrapher working in Halifax, Hamilton, and New York. In 1856 he became head of telegraphs in Nova Scotia for the New York, London and Newfoundland Telegraph Company, later the Anglo-American Telegraph Company. Mackay came to Newfoundland in January, 1857 as the local superintendent of operations which consisted of a telegraph line connecting with Cape Breton. Walking the length of the line, across the Island, he found a broken-down system and a dispirited work crew. Mackay ordered the repair of the line thus creating a valuable company asset with the laying of the submarine telegraph cable from Heart's Content, Newfoundland, to Valentia, Ireland in 1866. The company operated under a 50-year monopoly that expired in 1904. In 1867 Mackay had the whole telegraph line (which had originally cost $1,000,000) rebuilt from St. John's to Cape Ray for $90,000.

Mackay entered politics in 1878 as the representative for Burgeo and LaPoile. Elected by acclamation, he served in Premier William Whiteway's cabinet as a minister without portfolio from 1882 to 1884, lending great support to the building of a railway across Newfoundland. He was one of several Protestant politicians who left the Whiteway party in 1885 as a result of a violent confrontation between Protestants and Roman Catholics in Harbour Grace. Mackay's actions helped to bring about Whiteway's resignation and his replacement by Robert Thorburn, around whom Protestant support had rallied. In the 1885 general election Mackay won re-election as a Thorburn supporter, again by acclamation. When Whiteway was returned to the legislature in the 1889 election, Mackay did not stand again. On 24 December 1889 he was appointed by Whiteway to the Legislative Council. Whiteway also appointed him to the Fisheries Commission and as a Governor of the Newfoundland Savings Bank.

Mackay was the subject of a government inquiry in 1892 headed by Colonial Secretary Robert Bond into the operations of the public telegraph system which he had managed since 1877. The previous year the government had decided to have telegraph extensions built to various parts of the Island and Anglo-American erected the lines with the government providing the construction cost and the company being paid for any operating deficits for line extensions. Mackay personally contracted to build these lines and others in the late 1880s for a commission on their construction cost. The commission, however, was levied without any government authorization. In April 1891 the government accepted Mackay's offer to manage the government lines for one year for $18,000. In May 1892 he was appointed General Superintendent of the system.

The commissioners of the enquiry discovered that Mackay's management of the government telegraph accounts were intertwined with the accounts of Anglo-American and his personal bank account. The enquiry concluded that Mackay had misappropriated public funds and had falsified government vouchers and receipts on the public telegraph account. In March 1893 the government removed Mackay from his management of the public telegraphs and published the findings of the enquiry.

In the 1893 general election Mackay supported the Tory Party led by Moses Monroe and Walter Baine Grieve. The Whiteway Liberals won re-election but the Tories did not take defeat lightly. On 6 January 1894 they filed petitions in the Supreme Court under the Corrupt Practices Act of 1889 charging 17 government members with the illegal use of public funds during the campaign. Subsequent judgements of the court led to the unseating of the Whiteway government and the formation of a new one led by Tory merchant Augustus Goodridge who held office until 13 December of that year when the Liberals under Daniel Joseph Greene returned to office.

In 1894 Mackay sued the Liberal Evening Telegram alleging that the newspaper had libelled him. In late 1893 the newspaper had asserted that Mackay had used the telegraph system during the election campaign in support of the Tory party. The system was used free of charge by Tory supporters, while the Whiteway Liberals "had to adopt a private code in order to avoid publicity". In June 1894 Supreme Court Justice Sir James Winter found in favour of Mackay awarding him a verdict of $600 and costs.

Further government action against Mackay resulting from the report of the telegraph enquiry had proved difficult following the change of government in April 1894. Colonial Secretary Alfred Morine had reviewed the commission's report and dismissed it as a "grossly partisan and disgraceful document". He wrote Mackay that the Tory government had ordered a new investigation which would not only examine the content of the previous report but also the manner in which the commissioners had conducted their proceedings. The collapse of the colony's banking system later in December and the resultant financial and political problems and Morine's actions in June 1894, compromised any further action the new Liberal government could take against Mackay.

In May 1896 Governor Herbert Murray, who was determined to improve the image of the Legislative Council after several of its members - Thorburn, Augustus Harvey, and James Pitts - had been charged with conspiracy and larceny in the December 1894 collapse of Newfoundland's banking system and had resigned from the Council, forced Mackay to resign from the Council or else be removed by Murray. Mackay returned to active politics in 1900 when he successfully contested Port-de-Grave on behalf of Conservative Leader Alfred Morine but was defeated by incumbent Liberal Premier Robert Bond; Mackay was re-elected in 1904.

Mackay was also active in the social, cultural, and business life of his adopted country. As a member of St. Andrew's Presbyterian Church during the 1870s, he helped to promote a union of the conflicting Presbyterian factions in Newfoundland. In October 1883 he helped to found the City Club, a social club for leading city merchants, serving as president from 1883 to 1905, becoming Honorary President for Life in January of that year. From 1867 until his death Mackay was Provincial Grand Master of the Scottish Masonic jurisdiction in Newfoundland. On the commercial side, he was responsible in 1885 for Anglo-American establishing at St. John's the first public telephone system in Newfoundland. That same year he also helped fellow merchant Moses Monroe to establish a company (the St. John's Electric Light Company) that provided electric lighting for St. John's.

Mackay suffered a jaundice attack in May 1904 and his health never fully recovered. He died on November 24, 1905, at St. John's. His career naturally had revolved around the interests of his employer, Anglo-American, which he protected vigorously. For such devoted service, directors of the company had once given him a "handsome cabinet of silver".