He graduated from high school in Cambridge in 1875, then attended the United States Military Academy at West Point.

He later took charge of river improvements in the midwestern United States, including Wisconsin and Minnesota, as well as command of the Corps of Engineers' Sioux City District.

[1] In March 1875, Abbot received an at-large presidential appointment to the United States Military Academy (USMA) which was scheduled to begin in the summer of 1876.

[6] As with most top graduates of his era, Abbot received his choice of branch assignment, and selected the Corps of Engineers.

[6] He performed special duty in September 1886 when he was assigned to inspect and report on the serviceability of buildings in Charleston which had been damaged by an earthquake.

[6] In addition, Abbot took part in surveys of and improvements to coastal defenses in South Carolina, including Forts Moultrie, Sumter, and Johnson and Castle Pinckney.

[6] As part of improving defenses along South Carolina's coast, Abbot also oversaw design and construction of mortar batteries and disappearing gun carriages on Sullivan's Island, Charleston Harbor.

[6][b] He served on a combined civil and military board that planned improvements to the harbor of Brunswick, Georgia from November 1894 to June 1896.

[6] From September 1897 to October 1898, Abbot was in charge of river improvements in Wisconsin and Minnesota, including command of the Corps of Engineers' Sioux City District.

[6] During the Spanish–American War, he served on many boards which conducted surveys of harbors and coastal defenses in the eastern United States and made recommendations to improve them.

[6] In December 1901, he served on a board which considered options and provided recommendations for defenses at Apra Harbor, Guam, where some Filipino insurgent leaders had been deported as part of the Philippine–American War.

[6] From August 1903 to February 1907 he was in charge of manufacturing and distributing Taylor-Raymond 8, 10 and 12‑inch chain ammunition hoists so they could be installed at various coast artillery posts.

[6] Abbot was in charge of river, harbor, and fortifications projects in Rhode Island and Massachusetts from March 1911 to August 1912.

[6] From June 1911 to August 1912, he was a member of the board that considered fire control and searchlight positions for Narragansett Bay.

[9] In 1930, the U.S. Congress passed legislation permitting the general officers of World War I to retire at the highest rank they had held.