Alexander was born in 1880, the youngest child of Donald MacKillop and Margaret MacKillop of Baile. In 1900 his father was one of the men to receive a new croft in Borve, and the family moved to croft 12.

Alexander moved to Glasgow, becoming a clerk for Messrs Cooper. In 1929 he returned to Berneray to marry Catherine MacCuish, with whom he was to have a son. They made their home at Pol an Oir, at 19 Allotments.

Alexander became a merchant and grocer, and was district councillor for Harris. He was the man on Berneray responsible for marking the locally made tweed with the Orb mark and in 1938 was a representative on the Harris Tweed stand at the Empire Exhibition, held in Bellahouston Park, Glasgow.