Griffin studied law at Edinburgh University and the Middle Temple.
In 1774 Griffin returned to Virginia to practise his profession.
He took an interested part in pre-Revolutionary movements, but while asserting the rights of the colonies, hoped for a peaceful issue to the differences with England; and when again in London, on business, addressed to the Earl of Dartmouth, December 30, 1775, a “Plan of reconciliation between Great Britain and her Colonies. ”
He represented Lancaster in the Virginia legislature from May 1777 to May 1778, when he was elected a member of the Continental Congress, but his patriotic spirit chafed at the bickerings and delays of that body and he was distinctly relieved when Congress, April 28, 1780, appointed him judge of the Court of Appeals in Cases of Capture. He presided over this court until 1787, when, its business having dwindled after the conclusion of the war, it was abolished following provision for a more comprehensive federal judiciary; but not before Congress had passed a resolution “expressing their sense of the ability, fidelity, and attention of the judges”, and not before it had helped to further the beginnings of the United States Supreme Court by familiarizing the public mind with the idea of a superior tribunal of federal judicature.
Returned to the Virginia Assembly from Lancaster, 1786-87, Griffin was again elected to the Continental Congress and served as its president from January 22, 1788, until its dissolution. He had been one of the judges chosen by the states of Connecticut and Pennsylvania to preside over the provisional court that determined the ownership of the Wyoming Valley (1782); and his services in settling that important controversy may have led President Washington in 1789 to name him one of three commissioners to attend a treaty between the Creek Indians and the state of Georgia.
That same year he applied to Washington for “appointment in the diplomatic service or as a judge of the Supreme Court. ” The legislature of Virginia elected him a member of the Privy Council, but before he could qualify for that office, Washington - presumably seeking to strengthen the new government by a judicious choice, despite the charge of Federalist patronage - appointed him federal judge for the District of Virginia.
Before his death at Yorktown twenty-one years later, Griffin had beheld the business of the court mount steadily in quantity and importance, and he had helped preside over two of the most famous cases in the legal history of that period: the trial of James T. Callender for libel and that of Aaron Burr for treason.
Accomplished, upright, dependable, industrious, he enjoyed fully the confidence and respect of his age, but after his death his services and standing were undeservedly forgotten.
He was neither orator nor author; his work was not that which attracts popular notice; he has had no biographer; but, above all, he has been completely overshadowed by the giants who were his contemporaries.
His wife was formerly Lady Christina Stuart, eldest daughter of the sixth Earl of Traquair, with whom he had made a runaway marriage (1770) while in Edinburgh.