Griswold studied law with his father and was admitted to the bar in 1783. He began the practice of law in Norwich, Connecticut. He returned to Lyme in 1794 and was elected as a Federalist candidate to the Fourth United States Congress and to the five succeeding Congresses. Griswold served in Congress from March 4, 1795 until his resignation in 1805 prior to the convening of the Ninth Congress. During the Sixth Congress, he served as chairman of the Committee on Revisal and Unfinished Business and as a member of the Committee on Ways and Means.