Born in Glasgow, Scotland, Haughey received a limited education. Immigrated to the United States with his father, who settled in New York City. He moved to Jefferson County, Alabama, in 1841. While teaching in St. Clair County, studied medicine. He was granted a diploma by the New Orleans Medical College and engaged in practice at Elyton, Jefferson County, Alabama. He served as a surgeon in the Third Regiment, Tennessee Volunteer Infantry, in the Union Army 1862-1865. He resumed the practice of his profession in Decatur, Alabama. He served as delegate to the State constitutional convention in 1867. Upon the readmission of the State of Alabama to representation was elected as a Republican to the Fortieth Congress and served from July 21, 1868, to March 3, 1869. He was a candidate for renomination and while making a political speech was assassinated in Courtland, Alabama, on July 31, 1869, and died on August 5, 1869. He was interred in Green Cemetery, near Pinson, Alabama.