Abraham Murdock was born on September 20, 1810, in Massachusetts. He married a woman named Grace, and their daughter Elizabeth was born around 1842. They lived in Columbus, Mississippi, and Murdock worked as a merchant. By 1850, he owned $10,000 of real estate, and he enslaved at least four people. A decade later, he owned $20,000 of real estate and $30,000 of personal property, including at least three enslaved people.
Murdock sided with the Confederacy during the Civil War. In November 1860, he attended a county meeting and helped draft resolutions calling for secession. Murdock moved to Mobile, Alabama, in the 1860s. By 1870, he was president of the Mobile and Ohio Railroad Company, and he owned $100,000 of real estate and $100,000 of personal property. He returned to Columbus in the 1870s, and his wife died on July 21, 1880. He passed away in Eagle Pass, Texas, on July 17, 1888.