Born in Torrington, Connecticut, Griswold served in the militia during the Revolutionary War. After graduating from Yale College in 1786, he worked as a newspaper editor and pastor. After serving in the territorial government of Michigan from 1805-1808, Griswold moved to Ohio, and was appointed to the Senate to fill the vacancy created by the resignation of Edward Tiffin, serving from May 18, 1809 until a special election was held to choose a successor on December 11, 1809. Griswold then moved to the Illinois Territory, where he was appointed as a federal judge, serving on the bench and as a lawyer until his death.