Bronson Cutting was born in Oakdale, Long Island, New York on June 23, 1888. He attended the common schools and Groton School and graduated from Harvard University in 1910. Shortly after graduation, he became an invalid and moved to Santa Fe, New Mexico at the advice of his doctors to restore his health. He became a newspaper publisher in 1912 and published the Santa Fe New Mexican and El Nuevo Mexicano. From 1912 to 1918 he served as president of the New Mexican Printing Company, and of the Santa Fe New Mexican Publishing Corporation from 1920 until his death.

During the First World War Cutting was commissioned captain and served as an assistant Military Attaché of the American Embassy in London, England 1917-1918. He was regent of the New Mexico Military Institute in 1920 and served as chairman of the board of commissioners of the New Mexican State Penitentiary in 1925.

On December 29, 1927, he was appointed as a Republican to the United States Senate to fill the vacancy caused by the death of Andrieus A. Jones and served from December 29, 1927, until December 6, 1928, when a duly elected successor (Octaviano Ambrosio Larrazolo) qualified. He was not a candidate for election to this vacancy. However, his successor did not seek re-election, and Cutting was elected as a Republican on November 6, 1928, to the United States Senate, and won reelection in 1934. He died in a plane crash on his way back to New Mexico from Washington D.C. near Atlanta, Missouri, on May 6, 1935. Dennis Chavez was appointed to fill his seat in the Senate. Cutting is interred in Greenwood Cemetery, Brooklyn, New York.

Cutting is perhaps best known as the most prominent Anglo who sought to bring Hispanic voters into the political mainstream prior to the New Deal, and for maintaining correspondence with Ezra Pound in the 1930s.