Joseph Draper Sayers was born on September 23, 1841, in Grenada, Mississippi, to David and Mary Sayers. His father was a physician who owned $500 of real estate in 1850. He spent his early childhood in Tallahatchie County, Mississippi. His mother died in 1851, and the family moved to Bastrop, Texas, soon afterward.
He attended Bastrop Military Institute. He sided with the Confederacy during the Civil War, and on September 1, 1861, he received a commission as a 1st lieutenant in the 5th Texas Cavalry. He took part in the Battle of Valverde in New Mexico in February 1862, and he spent the next two years stationed in Texas and Louisiana. He was wounded in the Battle of Fort Bisland in April 1863 and again in the Battle of Mansfield in April 1864. He earned a promotion to major, and by 1864, he was serving as the assistant adjutant to General Richard Taylor.
Sayers returned to Bastrop after the war, and he married Ada Walton on March 5, 1868. She died on February 25, 1871, and he married amateur painter Orline Walton on February 20, 1879. He earned admission to the Texas bar in the late 1860s, and by 1870, he was working as a lawyer. That year, he owned $10,000 of real estate and $500 of personal property, and he employed at least one white domestic servant. He became a Democratic politician during Reconstruction, serving in the state senate from 1873 until 1875. He served as chairman of the Texas State Democratic Executive Committee and presided over the state Democratic Conventions in 1876 and 1878. He became lieutenant governor in 1879 under Oran M. Roberts, and he remained in office for the next two years.
Voters elected Sayers to the United States Congress in 1884. He served until 1899, when he became governor of Texas. He left office in 1903 and returned to his legal practice. He served on the Board of Regents for the University of Texas and sat on the Industrial Accident Board and the State Board of Legal Advisors. He died in Austin, Texas, on May 15, 1929.