Mechem was born in Ottawa, Franklin County, Kansas to Homer C. Mechem and Martha (Davenport) Mechem.
On the twelfth of February, 1910, in Santa Fe, Judge Mechem was married to Miss Eleanor Frances O’Hara, a native of Chicago, Illinois.
He was admitted to the bar in 1893. After practicing law in Fort Smith, Arkansas for ten years, he moved his law practice to Tucumcari, New Mexico at the age of thirty-two in 1903.
Mechem was appointed by Governor Otero as the district attorney for Quay and Guadalupe Counties of New Mexico, a position he held from 1905 to 1909, being reappointed by Governor Hagerman. He also served as a member of the New Mexico Territorial Council from 1909 to 1911. In 1909 President Taft appointed him a justice on the New Mexico Territorial Supreme Court where he served until 1911. Thereafter he served as a district judge for the Seventh Judicial District in Socorro until1920, being twice re-elected.
In September 1917 in a famous attempt to silence the press Judge Mechem convicted the editor of the New Mexican of criminal contempt for publishing a story about the judge’s affidavit in a separate libel case against the newspaper. The contempt conviction was speedily reversed, but the underlying libel case was not dismissed until October 1919.
In 1920 he became the Republican candidate for governor and won by the largest percentage vote of any previous New Mexico gubernatorial election. He decided not to run for a second term.
In 1923 he opened his law practice in Albuquerque which he maintained until his death. His law offices were in the First National Bank building where he later associated with another former governor, Arthur T. Hannett. He served a term as president of the state bar association, and was a ranking Mason, an affiliate of the Scottish Rite bodies and holder of the thirty-second degree of the Scottish Rite at Santa Fe. He was also a member of the Benevolent and Protective Order of Elks, Sons of the American Revolution, the American Bar Association, and the Albuquerque Lawyers Club.