Wotherspoon was born in Washington, D.C., on November 16, 1850, the son of Army surgeon Alexander Summerville Wotherspoon and Louisa Kuhn Wotherspoon. Alexander Wotherspoon was a veteran of the Mexican War; in addition to serving on Winfield Scott's staff, he was present when President Zachary Taylor became ill in 1850, and treated Taylor during his final illness. William Wotherspoon was educated in private schools and served aboard ship as a mate in the United States Navy from 1870 to 1873.
In 1898, while on recruiting duty at Fort McPherson, he organized the 3rd Battalion, 12th Infantry. He served in the Philippines against insurgents and as collector of customs at Iloilo from 1899 to 1901.
Senior command
In 1901, he was promoted to major and transferred to the 30th Infantry. He commanded the 2nd Battalion, 6th Infantry at Fort Leavenworth and then taught at the Command and General Staff College from 1902 to 1904. He was promoted to lieutenant colonel and assigned to the 14th Infantry in 1904 and later was transferred to the 19th Infantry and became the director of the U.S. Army War College from 1904 to 1906. Wotherspooon was the chief of staff of the Army of Cuban Pacification from 1906 to 1907. Wotherspoon served as the acting president of the Army War College and chief of the Third Division, General Staff in 1907. He was promoted to brigadier general in October 1907, advanced over 140 officers with more seniority. He was president of the Army War College, serving from 1907 to 1909 and again from 1910 to 1912. Wotherspoon was largely instrumental in transforming the Army War College from an adjunct of the General Staff to an autonomous educational institution, he became assistant to the chief of staff from 1901 to 1910 and again in 1912 to 1914. He was promoted to major general in May 1912 and served as the commander of the Department of the Gulf until that September.
Wotherspoon became the Chief of Staff of the United States Army in 1914; he served from April 21 to November 15. During his term, he highlighted the shortage of experienced officers and noncommissioned as the Army began to prepare for possible involvement in World War I. He also emphasized the need to improve coastal defenses to match battleships that were increasing in size and armament, oversaw establishment of the Army's first aviation section as a branch of the Signal Corps, and completion of the Panama Canal and its opening to ship traffic.
In 1887, while stationed in northern New York, he married Mary C. Adams of Utica, New York. They were the parents of a son, Alexander Somerville Wotherspoon. Alexander Wotherspoon was a career officer in the United States Navy, and retired as a rear admiral.