Andrew J. Alexander was born around 1842 in Woonsocket, Rhode Island, to William and Mary Alexander. His father was a machinist. The family eventually moved to Boston, Massachusetts, and by the early 1860s, he was living in Franklin, Massachusetts. He earned a living as a carpenter.
He enlisted in the Union army on September 15, 1862, and he mustered in as a private in Company C of the 45th Massachusetts Infantry on September 26. According to his service records, he was 5 feet, 7¾ inches tall, with light hair and blue eyes. The regiment was stationed in North Carolina, and it took part in the Battle of Kinston.
and he mustered out on July 3, 1863. He returned to the Union army the following year, mustering into the 14th Massachusetts Light Artillery on February 27, 1864. The regiment took part in the Overland Campaign and the siege of Petersburg. He eventually earned a promotion to corporal, and then to sergeant, but he was demoted to corporal in May 1865. He mustered out on June 15, 1865.
He returned to Massachusetts after the war, and he married Olive E. Legg on March 3, 1866. They had at least two children: Andrew, born around 1868; and William, born around 1872. The couple was living apart in 1870: she was living with her parents in Blackstone, Massachusetts, while he was living with his sister Anna in Boston.
The couple eventually got divorced, and he married Mary A. Crowell on January 1, 1886. They had at least two children: Loretto, born on January 12, 1889; and Annie, born on January 13, 1890. His wife died on October 11, 1899. He lived in Boston, Massachusetts, and continued to work as a carpenter. By 1910, he was living in a National Home for Disabled Volunteer Soldiers in Chelsea, Massachusetts. A decade later, he was living with his daughter Annie in Cambridge, Massachusetts. He died in Boston on June 7, 1926.