Samuel Hollingsworth Stout was born on March 03, 1822 in Nashville, Tennessee, to Katherine Tannehill and Samuel Van Dyke Stout. He was educated first at the University of Nashville, and graduated with a BA in 1839 and again with an MA in 1843. He studied medicine with his brother (Josiah Stout) in 1844 and taught school in Elkton, Tennessee, between 1844 and 1847.

Stout studied medicine formally at the University of Pennsylvania, from whence he graduated with his M. D. in 1848. In the same year, he married Martha Moore Abernathy. He then practiced medicine in Nashville before retiring with his family to Giles County, Tennessee, in 1850. Here, he farmed and continued to practice medicine until he entered the Confederate Army as a surgeon in May of 1861. He rose through the ranks quickly, and was named the Medical Director of Hospitals of the Department and Army of Tennessee in February of 1863.

In this position, Stout demonstrated a particular gift for navigating the Confederate government bureaucracy. He was well versed in army medicine, having passed the naval surgeon's exam and studied army regulations while in private practice. It was this knowledge that enabled him to bypass enormous amounts of red tape, to the great benefit of his patients. For example, Stout knew of an obscure regulation that allowed hospitals to claim the money value of any rations allotted for their patients that they did not draw. By enforcing this regulation, Stout collected millions of dollars that he then used to improve the hospitals in his jurisdiction. He also purchased a printing press to create the forms necessary to run the hospital, and even enlisted a convalescent potter to make the hospital's dishes. The hospital quickly had more dishes than it could use, and Stout traded these to local farmers for extra food. Stout also constructed his hospitals so that they could be dismantled and moved quickly, thus enabling him to keep up with the Confederate Army's nearly constant southern retreat, and introduced isolation wards for patients with communicable diseases.

After the war, Stout returned to his family in Giles County. He practiced medicine there until 1869, when he moved to Atlanta. He moved again in 1873, this time to Roswell, Georgia. In both of these places, Stout fought for a system of public schools. He continued this crusade after moving to Cisco, Texas in 1882, and was named the U. S. Commissioner of Education in 1893. Stout was also a prolific writer during these years, writing articles on military medicine, general surgery, and historical causes. Stout died on September 18, 1903 in Clarendon, Texas.