Born near Cruden, Aberdeenshire, Scotland in 1745, Smith attended the University of Edinburgh, and then immigrated to the United States, where he settled in Bedford, Pennsylvania on February 9, 1769.
When the Revolutionary War broke out, Smith served as a deputy colonel of a militia unit.
Smith died in Philadelphia on March 31, 1809 and was buried in Christ Church Burial Ground.
While serving as a justice on the Supreme Court of Pennsylvania, Smith was impeached on March 23, 1804 by the Democratic–Republican-led Pennsylvania House of Representatives, along with two other Federalist justices of the Supreme Court, Edward Shippen IV and Jasper Yeates.
The justices were not removed, being acquitted in their impeachment trial before the Pennsylvania Senate in the vote held on January 28, 1805.