He attended the district school and the academy at Mitchell, and at the age of sixteen received an appointment as cadet at the United States Naval Academy at Annapolis, but failed to pass the physical examination. He taught school for a time, spent three years in Franklin College (Indiana), and one year at DePauw University at Greencastle.
In 1874 Burton began to read law in the office of Gordon, Brown & Lamb, at Indianapolis, and in 1875 was admitted to the bar. In the spring of that year he married Mrs. Carrie (Mitchell) Webster of Princeton. In 1876 Mr. Burton was nominated by the Republicans for presidential elector and made many speeches during the campaign. In 1878 he moved to Abilene, Kansas, where he formed a partnership with Judge John H. Mahan for the practice of law.
He was elected to the Kansas House of Representatives in 1882; was re-elected in 1884 and again in 1888; and was appointed a member of the World's Fair Columbian Commission at Chicago in 1893, representing Kansas. In 1895 Burton lacked but one vote of being the Republican Party nominee for United States senator. But in January, 1901, he was elected senator and served from March 4, 1901, until June 4, 1906, when he resigned. While in the Senate, he was chairman of the Committee on Forest Reservations and Game Protection (Fifty-seventh and Fifty-eighth Congresses).
On January 23, 1904, Burton was indicted by a Federal grand jury at St. Louis, Missouri, on the charge of having accepted $2,500 from the Rialto Grain and Securities company (a “get-rich-quick” concern), of that city, to use his influence with the post office department to prevent the issuance of a fraud order against the company, which would deny it the use of the U.S. mails.
Burton was tried before Judge Adams of the U.S. district court at St. Louis in March, found guilty and sentenced to pay a fine of $2,500 and serve six months in the jail at Ironton, Missouri. Burton's defense was that he was acting within his rights, and that the money received from the company was nothing more than he was entitled to as attorneys fees. He appealed the case to the United States Supreme Court, which in January, 1905, reversed the decision of the district court, on the grounds that the money was paid to Burton in Washington, and remanded the case for a new trial.
The second trial was before Judge Van Devanter of the United States circuit court at St. Louis in November, 1905, and resulted in the same sentence as that imposed by Judge Adams's court. A second appeal to the Supreme Court followed, and this time the decision of the lower court was sustained.
After his resignation he returned to his law practice in Abilene and engaged in the newspaper and real estate development businesses.
Joseph Burton died in Los Angeles, California in 1923; the body was cremated and the ashes deposited in the columbarium of the Los Angeles Crematory Association. The ashes were removed in 1928 for burial in the Burton family plot in Abilene Cemetery.