Sir Alexander Buchanan was the eldest of the three sons of Sir Walter Buchanan, eleventh Laird of Buchanan.
Sir Alexander fought in the Battle of Baugé on 21 March, 1421, in which the Kingdoms of Scotland and France fought and won against the Kingdom of England - a major defeat for the English during the Hundred Years' War. The English were led by Thomas of Lancaster, 1st Duke of Clarence, second son of King Henry IV of England and his first wife, Mary de Bohun and brother of the current King, Henry V of England. During the battle Sir John Carmichael of Douglasdale broke his lance unhorsing the Duke of Clarence. Once on the ground, the Duke was slain by Sir Alexander. Sir Alexander held the prince's coronet aloft on his lance, bringing such dismay to the English that the battle was lost to them. In recognition of this the Clan Buchanan coat of arms to this day depicts a ducal coronet being held up in triumph.
Sir Alexander died without issue and his father, Sir Walter Buchanan, eleventh Laird of Buchanan, was succeeded by his second son, Sir Walter Buchanan, twelfth Laird of Buchanan.