Joseph Andrews was born in April 1833, in Providence, Rhode Island, to George L. Andrews and Cornelia Lippitt. His father died around 1838. He grew up and attended school in Providence before moving to Springfield, Iowa, sometime in the 1850s. By 1860, he was working as a farmer, and he owned $1,600 of real estate and $600 of personal property. He enlisted in the Union army on September 23, 1861, and mustered in as a captain in Company F of the 8th Iowa Infantry later that day. He was promoted to major on February 7, 1862, and he was wounded in the neck in the Battle of Shiloh on April 6, 1862. He resigned on January 26, 1863. In 1864, he attempted to rejoin the army in command of a regiment, but he was apparently unsuccessful.
Andrews married Emeline Dunbar around 1863, and they had at least six children: Elizabeth, born around 1866; Cornelia, born around 1868; Joseph, born around 1870; Francis Dunbar, born around 1870; Howard, born around 1872; and Warren, born around 1875. They lived in Davenport, Iowa, and Andrews worked as an auctioneer. By 1870, he owned $5,000 of real estate and $2,000 of personal property. A decade later, he was serving as a clerk of court. He died in Davenport on May 26, 1893.