Mark Alexander, a younger son of Robert Boyd of Pinkill in Ayrshire, was born on the 13th of January 1562. He is said to have come into the world provided with a couple of teeth. He learned the rudiments of the Latin and Greek languages at Glasgow under two grammarians, but was of so high and untractable a spirit, that they despaired of ever making him a scholar. Having quarrelled with his masters, he beat them both, burnt his books, and forswore learning. His uncle, James Boyd of Trochrig, was at that time archbishop of Glasgow; and, as he soon lost his father, his academical studies were conducted under the superintendence of this relation. After he entered the university, he was engaged in some very riotous proceedings, which have been particularly detailed by the able biographer of Melville. While he was yet a youth he followed the court, and exerted the usual means of obtaining preferment; but the fervour of his temper soon precipitated him into quarrels, from which he came off with honour and safety, though frequently at the hazard of his life. As he was nearly related to Lord Boyd, it is probable that he relied chiefly on his patronage; but, as Lord Hailes remarks, "all that we learn of his proficiency at court is, that he fought one duel, and was engaged in numberless broils." With the approbation of his friends, he went to serve in the French army, and carried with him his little patrimony, which he soon dissipated at play. He was shortly after roused by that emulation which is natural to superior minds, and applied himself to letters with unremitting ardour, till he attained to no mean proficiency as a scholar. Leaving his native country in 1581, when only in his twentieth year, he was not yet past the age of academical study; and he attended the lectures of several professors in the university of Paris, particularly those of Passerat, professor of eloquence, and of Genebrand, professor of Hebrew. Having next directed his attention to the civil law, he went to Orleans, and became a pupil of J. Robert, "a man principally known for having dared to become the antagonist of Cujacius." But from the university of Orleans he speedily removed to that of Bourges, where he is said to have obtained the friendship of Cujacius, by writing some verses in obsolete Latin; and, as one of his biographers has suggested, that learned man could not fail to relish verses which approached the standard of the twelve Tables.

The plague having driven him from Bourges, he sought a place of refuge at Lyon; and, when the infection extended to that city, he retired into Italy, where he contracted a friendship with a person whom he names Cornelius Varus. Having been seized with an ague, he returned to Lyon to try the effect of change of air; and the only regret which he felt in quitting Italy, is said to have arisen from his being thus deprived of the literary conversation and salutary advice of his friend. It was about the year 1585 that he revisited France. In 1587 he served with the royal forces opposed to the mercenary army of Germans and Swiss, which had invaded that country to support the king of Navarre. He served under an officer of cavalry, who was a Greek by birth; and, during this campaign, he was wounded by a shot in the ankle. In 1588 he took up his abode in Toulouse, and applied himself to the study of the civil law under Roaldes, a professor of eminence. About the same period he appears to have written several tracts on the science of jurisprudence, and even to have projected a systematical work on the law of nature and nations. But his studies met with an unforeseen interruption, in consequence of the tumults which ensued at Toulouse, and during which the first president Duranti, the advocate-general Dafis, and other individuals of inferior quality, were murdered by the inhabitants. During this season of outrage Boyd was thrown into prison; and, as innocence afforded him no security, he was exposed to imminent danger of his life; but he owed his deliverance to the intercession of some of his friends. He now retired to Rochelle; but as the climate did not agree with his constitution, he afterwards fixed his residence at Fontenay in Poitou. In this retreat he devoted much of his time to study, and occasionally resumed the avocation of a soldier, for which he retained a violent propensity. He is reported to have acted as preceptor to a young French gentleman of the reformed religion, but of such an engagement his own writings communicate no information. About the year 1591 he appears to have formed a design of reading lectures on the civil law; and the heads of his prelections on the Institutes of Justinian are still preserved among his other papers in the Advocates Library.

His friends in Scotland, and among others Patrick Sharpe, under whom he had studied in the university of Glasgow, urged him to return to his native country; but, according to his own account, the state of his health had long obliged him to live obscurely in France, and his scanty circumstances would not allow him to make a tolerable figure in Scotland. He endeavoured however to strengthen his interest in his native land, by dedicating to James the Sixth a collection of his poems and epistles, printed at Antwerp, 1592, in 12mo. Three years afterwards, while preparing to return home, he received intelligence of the death of his elder brother William, for whom he apparently cherished a very sincere affection. Of his subsequent history, few particulars have been recorded. We are however informed that he at length returned to Scotland; and, after a short residence having undertaken to accompany the earl of Cassilis in his travels, he completed this engagement, and once more revisited his native country, where he died of a slow fever, on the 10th of April 1601. At the time of his death he was only in the fortieth year of his age.

Boyd appears to have been a person of a restless and turbulent disposition; and, as he added courage to strength, his sword must at least have been as formidable as his pen. He was tall, robust, and well-proportioned, and, possessing a handsome and pleasing countenance, he had much of the gallant bearing of a soldier. His literary vanity was not the least conspicuous part of his character. He was however a man of genius; and if his disposition and circumstances had been more favourable for persevering and systematic exertion, he might have secured a high reputation among the scholars of the age.