Clark, the son of famed explorer William Clark, was born 10 January 1809 in St Louis, Missouri. He was named for the elder Clark's partner Meriwether Lewis. The younger Clark attended West Point, graduating 23rd in the class of 1830. He served three years in the artillery, including in the Black Hawk War, before resigning to become an architect, civil engineer and legislator.

Clark is most noted for designing the St Louis Theatre which opened in 1837, the first genuine theater west of the Mississippi and as the US Surveyor General of Missouri. He commanded a volunteer artillery unit during the war with Mexico. 

When the Civil War began Clark was named a brigadier general in the Missouri State Guard and was given command of Missouri's 9th Military District in the latter part of 1861. On 17 July 1861 he was named chief of artillery in Missouri's Department #2. In March 1862 Clark was appointed major in the Confederate States Army. He served as Sterling Price's chief of artillery until April 1862 then was appointed colonel of artillery on the staff of Braxton Bragg. Clark commanded Bragg's artillery at Stones River. In August 1864 Clark was assigned to the ordnance department as an inspector. He would remain in this post until the end of the war.

Following the war Clark became commandant of cadets and professor of mathematics at the Kentucky Military Institute. He died 28 October 1881 in Frankfort, Kentucky and is buried in St Louis next to his famous father.