Helm began working as a lawyer in Colorado Springs, Colorado in 1875. He was elected to the Colorado House of Representatives in 1877 and to the State Senate in 1879, representing El Paso County in both offices. He became a district judge in 1880. He was elected to the Colorado Supreme Court in 1882 and re-elected in 1891. He served as chief justice from 1889 to 1892. Helm resigned from the supreme court in 1892 to run for Governor of Colorado as a Republican. He was his party's nominee but was defeated by Populist Party politician Davis Hanson Waite. Helm practiced law until his death, except for a period from 1907 to 1909 when he was appointed by Governor Henry Augustus Buchtel to fill a vacancy on the Supreme Court. As an attorney, he represented the interests of the Moffat Tunnel, Moffat estate and Moffat railway. Another client, beginning in 1904, was the Chicago, Rock Island and Pacific Railroad. He had an office in the Equitable Building. He married on September 27, 1881 to Marcia Stewart of Wisconsin. Her family moved to Colorado Springs in 1874 for her father George H. Stewart's health. They did not have any children. Her sister was Alice Stewart Hill, the wife of Francis B. Hill, was an artist and art instructor of Colorado Springs. Helm was a member of a number of organizations. He died May 13, 1915 at his home in Denver and is buried in there in the Fairmount Cemetery in a large mausoleum, where he was interred following public funeral services in Denver. After Joseph died, Marcia lived part of the time with her sister Hattie in Colorado Springs. Marcia died in 1932 and is also buried in the mausoleum at Fairmount Cemetery.