Mondragon was born in Antonito, Colorado, and raised in the Española Valley region of New Mexico.
[1][2] Mondragon was an autodidact on bass, and began working professionally in Los Angeles.
[3] He served in the United States Army during World War II, and then joined Woody Herman's First Herd in 1946.
Over the next two decades, he became one of the more popular studio bassists for jazz recording on the West Coast, appearing on albums by June Christy, Shorty Rogers, Shelly Manne, Buddy Rich, Buddy DeFranco, Marty Paich, Claude Williamson, Georgie Auld, Chet Baker, Bob Cooper, Harry Sweets Edison, Gerry Mulligan, Art Pepper, Bud Shank and Ella Fitzgerald.
[4] With Georgie Auld With Chet Baker With Louie Bellson With Buddy Bregman With Hoagy Carmichael With Bobby Darin With Harry Edison With Herb Ellis and Jimmy Giuffre With Astrud Gilberto With Johnny Hartman With Woody Herman With Lena Horne With Harry James With Stan Kenton With Barney Kessel With Peggy Lee With Henry Mancini With Shelly Manne With Warne Marsh With Carmen McRae With Sérgio Mendes With Jack Montrose With Gerry Mulligan With Mark Murphy With Oliver Nelson With Art Pepper With Jane Powell With Shorty Rogers With Pete Rugolo With Lalo Schifrin With Bud Shank With Carly Simon With Frank Sinatra With Paul Williams