Mensch studied bass with former New York Philharmonic principal bassist Anselme Fortier at the ManhattanSchool of Music. As a teenager, he played with the Dick Messner Big Band at the Hotel McAlpin in order to pay for his bass lessons. He was an excellent tennis player in his youth, and originally wanted to pursue a career in tennis. However, he was also a promising bassist and eventually chose music over tennis. "This was at the start of the Great Depression", he told the Juilliard Journal, "so pursuing a career in music was pretty risky. I was lucky that my parents didn't try to make me go into a field that was a safer bet." Mensch joined the Pittsburgh Symphony in 1932 after winning the audition on the stage of Carnegie Hall in front of Otto Klemperer. He was assistant principal bass under Klemperer and Fritz Reiner until 1938. He then joined the New York Philharmonic under John Barbirolli. In 1943, Mensch left the Philharmonic to serve in the U.S. Army in Texas, during which time he played bass in the U.S. Army Band. In 1944, Mensch returned to New York as a freelance musician. He subsequently performed with the NBC Symphony under Arturo Toscanini and played in numerous television and radio shows. He recorded with Gregor Piatagorsky, Isaac Stern, Nathan Milstein, the Bach Aria Group, the Casals Festival Orchestra, the Columbia Symphony, and on every commercial recording made in NY. He also recorded with Frank Sinatra, Barbra Streisand, Paul McCartney, and numerous others. Mensch can also be heard on many soundtracks from the 1940s until the 1970s. For example, the theme from the 1975 film Jaws is played by Homer Mensch. At the request of the New York Philharmonic's then-conductor, Leonard Bernstein, Mensch returned to the Philharmonic in 1966. He remained until 1975, playing under Bernstein and Pierre Boulez. After leaving the Philharmonic, he served as principal bass of the Mostly Mozart Festival Orchestra, the New York Chamber Symphony, the New York Choral Society, Little Orchestra Society, and the New York Pops. ;Teaching career Mensch joined the Juilliard faculty in 1970 and became the chair of the double bass department in 2002. He joined the Manhattan School of Music faculty in 1980 and received MSM's Presidential Medal for Distinguished Service in May 2005.
Notable students
Nathaniel Ayers, homeless cellist, subject of the book and movie, The Soloist, was Mensch's double bass student while at Juilliard; Mensch was his mentor