Smith was born on August 13, 1805 in Hartford, Connecticut, United States, and attended Hartford public schools. He graduated from Yale University at the age of 19 where he was a member of Phi Beta Kappa Honor society. Smith taught briefly in a private school in Salisbury, North Carolina and then attended medical school at Yale graduating as medical doctor in 1828. He later lived in France and during the Paris cholera epidemic of 1832, Smith helped to treat the sick and wrote a pamphlet on the disease. Returning to the United States, Smith began his medical practice in Salisbury, North Carolina. He became active politically and part owner of the nullification newspaper the Western Carolinian. In the fall of 1836, Smith was persuaded to move to Texas by J. Pinckney Henderson, Henderson, who would later become the first Governor of Texas, had been a a friend of Smith's while living in Salisbury. Upon arriving in Texas in 1837, Smith quickly became a close acquaintance of Sam Houston and was appointed to the post of surgeon general with the Republic of Texas Army. Smith set up an efficient system of medical operations and established the first hospital in the area that would later become the city of Houston. Smith was a charter member and first vice president of the Philosophical Society of Texas. The society immediately set about to request that the Texas Congress establish a system of public education in Texas. In 1839, a yellow fever epidemic broke out in Galveston, and Smith treated the victims of the disease while writing reports about the treatment of the disease in the Galveston News. As a result of this experience, he wrote the first treatise on yellow fever in Texas. He purchased land near Galveston Bay and built his plantation, Evergreen, in southeast Harris County. During the Mexican-American War (1846-48), Smith served as a surgeon in the U.S. Army on active duty with Gen. Zachary Taylor in the field. After the War with Mexico Smith returned to Texas and in 1853, helped establish the Texas Medical Association. In 1855, Smith was elected to the Texas House of Representatives from Harris County.

Smith supported Texas' secession from the Union in 1861. When it was clear that war was inevitable, he organized the Bayland Guards, also known as Company C of the 2nd Texas Infantry. He outfitted and drilled the company, and the men elected Smith as their captain. While commanding Company C at the Battle of Shiloh in 1863, Smith received a severe arm injury. Because of the gallantry of the 2nd Texas Infantry at Shiloh, Colonel John C. Moore was promoted to Brigadier General in charge of the 2nd Brigade, Maury's division and later in Vicksburg in Forney's Division. Smith was brevetted a Colonel and was given command of the 2nd Texas Infantry Regiment. At the Battle of Vicksburg, the regiment was distinguished for its defense of a crescent-shaped fortification, which came to be known as the Second Texas Lunette. The fortification was located in the center of the Vicksburg line of defense. Under the command of Colonel Smith, the 2nd Texas Infantry withstood two Union assaults of brigade strength directed against the lunette on May 22, 1863. After the surrender of Vicksburg on July 4, 1863, Smith was in charge of defenses in the vicinity of the Matagorda Peninsula on the Texas Gulf Coast and finally at the end of the war, the remnants of Second Texas was charged with defending the port of Galveston from Union invasion. Ashbel Smith died January 21, 1886 and is buried in the Texas State Cemetery in Austin, Texas.