Alexander W. Acheson, soldier, mayor, and physician, was born to Judge Alexander Wilson and Jane (Wishart) Acheson on October 12, 1842, at Washington, Pennsylvania. In 1861 he entered the Civil War as a private in the Thirteenth Pennsylvania Regiment. He was transferred to the 140th Pennsylvania Regiment during the following year and with this unit rose to the rank of sergeant in 1862 and captain in 1863. As a captain he served as aide-de-camp to Gen. Nelson A. Miles. Acheson was the first United States Army officer to mount captured breastworks at the center of the Confederate lines at the battle of Spotsylvania, Virginia, in May 1864. He was shot in the face during the course of this five-day battle but survived the injury.
At the end of the war Acheson returned to his hometown, where the local university, Washington and Jefferson College, awarded him an honorary A.B. degree. He received the M.D. degree from the University of Pennsylvania the following year. He established a practice in Philadelphia in 1872 but abandoned it the same year and moved to Denison, Texas. Apparently aware of the benefits that the Grayson County town derived from the presence of the Missouri, Kansas and Texas Railroad, which extended its tracks into Denison from Oklahoma in 1872, Acheson secured an interview with railroad magnate Jay Gould. During this meeting he argued successfully for the building of the tracks of Gould's Texas and Pacific Railway through Denison. Acheson served four terms as mayor of Denison. He ran unsuccessfully as the Republican nominee for governor in 1906, for the United States Senate in 1916, and for the United States House of Representatives in 1920. He served as city physician of Denison from 1923 through 1929 and sat on the boards of directors of the local State National Bank and the Denison and Suburban Railway.
As a staunch advocate of efforts to make the Red River navigable and to control its flooding, Acheson was an honorary lifetime vice president of the Red River Flood Control and Navigation Association. He also served as the Texas director of the Mississippi Valley Association and as a delegate to conventions on rivers at New Orleans, Washington, and Chicago.
He married Sarah M. Cooke on June 20, 1864; they had a daughter. Acheson was a Presbyterian and a member of the Benevolent and Protective Order of Elks, the Knights of Pythias, and various state and national medical associations. He was also the only honorary member of the Veterans of Foreign Wars in North Texas. He died at his home in Denison on September 7, 1934.