Joseph Underwood was born in Goochland County, Virginia, the brother of Warner Lewis Underwood. He moved to Barren County, Kentucky in 1803 and lived with his uncle. He attended the common schools and graduated from Transylvania College in Lexington, Kentucky in 1811. He studied law in Lexington, but his studies were interrupted by the War of 1812, in which he served as a Lieutenant in the Thirteenth Regiment of the Kentucky Infantry. He was admitted to the bar in 1813 and commenced the practice of law in Glasgow, Kentucky.

Underwood served as town trustee and county auditor until 1823. He was a member of the Kentucky House of Representatives from 1816 to 1819. He moved to Bowling Green, Kentucky in 1823, and again was a member of the State House of Representatives from 1825 to 1826. He ran unsuccessfully for lieutenant governor of Kentucky in 1828, and served as a judge of the Court of Appeals from 1828 until 1835.

Underwood was elected as a Whig to the United States House of Representatives, serving Kentucky's District 3 from March 4, 1835 until March 3, 1843. There he was chairman of the U.S. House Committee on the District of Columbia. He declined to be a candidate for renomination in 1843, and resumed the practice of law. He was a presidential elector on the Whig ticket in 1844, and again joined the State House in 1846, where he served as speaker.

Underwood was next elected as a Whig to the United States Senate and served from March 4, 1847 to March 3, 1853, when he did not run for reelection. He was elected to the State House yet again, serving from 1861 to 1863. He died near Bowling Green and was interred in Fairview Cemetery. Joseph Underwood was the grandfather of Oscar Wilder Underwood.