Born in Wallula, (an unincorporated community just south of
Lansing),
Kansas, Mellott received a
Bachelor of Laws from the
Kansas City School of Law (now the
University of Missouri–Kansas City School of Law) in 1917. He was an
Assistant United States Attorney for the District of Kansas from 1917 to 1918, and was in private practice in
Kansas City, Kansas from 1919 to 1922. He was a Judge of the City Court of Kansas City from 1923 to 1924, and a county attorney in Kansas City from 1927 to 1929. During the time he was in private practice and during his initial tenure as a judge for the City Court of Kansas City Arthur Mellot also returned to Kansas City School of Law to teach. It is likely that during this time teaching at his alma-mater Mellot first encountered
Harry S. Truman. From 1934 to 1935 he was a deputy commissioner of internal revenue in
Washington, D.C. He was appointed to the United States Board of Tax Appeals in 1935, serving until 1942 when that body was converted to the
United States Tax Court, serving as a Judge of that court until 1945. ==Federal judicial service==