Stone was born near Richmond, Kentucky on May 7, 1848, and attended Richmond's public schools as a child; he graduated from the University of Missouri at Columbia in 1867, whereupon he began the study of law. Admitted to the bar in 1869, he began practice that year in Bedford, Indiana. Soon he moved back to Columbia, where he was the city attorney for a time in 1870. Later that year he moved to Nevada, Missouri, and continued his practice, becoming the Vernon County prosecuting attorney from 1873 to1874 and was a presidential elector for the Democratic ticket in 1876. In 1884 Stone was elected to the House of Representatives, where he served until 1891; he did not seek renomination in 1890. In his time there he served as the chairman of the Committee on War Claims. From 1893 to 1897 he served as Missouri's governor, moving to Jefferson City in 1893. Beginning in 1896 he served as a member of the Democratic National Committee, serving in this capacity until 1904; he was the committee's vice-chairman from 1900 until his departure. In 1897 Stone moved to St. Louis, where he continued his practice; he returned to Jefferson City in 1903. In 1902 he was elected to the Senate, being reelected in 1908 and serving until his death. In his time, he served as the chairman of the Committee on Additional Accommodations for the Library, and also served on the Committee on Revolutionary Claims, the Committee on Corporations Organized in the District of Columbia, the Committee on Foreign Relations, and the Committee on Indian Affairs. Stone died in Washington, D.C. on April 14, 1918; he is buried in Nevada, Missouri. His seat was filled until the 1918 election by Xenophon P. Wilfley.