Jiří Mráz was born September 9, 1944, in Písek, a small town in southern Bohemia, and started on violin at seven. At twelve he heard Louis Armstrong on a Voice of America broadcast, the standard route into jazz for a Czech teenager under a government that treated the music as suspect, and he began playing jazz in high school, first on alto saxophone. He switched to double bass a few years later and studied the instrument at the Prague Conservatory under Professor František Hertl from 1961 to 1966, a conservatory grounding in orchestral bass technique that stayed audible in his playing for the next fifty years. His first professional work came in guitarist Rudolf Dašek's trio and then in Karel Velebný's SHQ, the leading modern-jazz group in Czechoslovakia, with whom he made his earliest records: SHQ a přátelé (1965), Jak hrál S+HQ (1966), and tracks on the state label's Československý jazz 1965 and 1966 surveys, all credited to Jiří Mráz. In 1966 he took part in the international competition for modern jazz that pianist Friedrich Gulda staged in Vienna, judged by a panel that included Ron Carter, Mel Lewis, Cannonball Adderley, Art Farmer, J.J. Johnson, and Joe Zawinul. He placed in the bass category, and the prize carried a scholarship to the Berklee School of Music in Boston.

He left Czechoslovakia in 1968, the year Warsaw Pact troops ended the Prague Spring, and did not go back to live there. He spent several months in West Germany, mostly in Munich, where he worked alongside the American expatriates Mal Waldron, Leo Wright, and Benny Bailey, and turned up at the Domicile club in a quartet with saxophonist Pony Poindexter and his fellow Czech émigré Jan Hammer, a night that survives on record as New Orleans Fire (Live 1969). He took up the Berklee scholarship in the autumn of 1968, adopted the Americanised spelling "George Mraz" there, and is listed by the school as class of 1970. Boston work started immediately: pianist Ray Santisi hired him for a regular gig on his first day. In 1969 Dizzy Gillespie called him to New York, and he became a U.S. citizen in 1973.

The first job that made his name internationally was the Oscar Peterson trio, which he held from 1970 to 1972 and which put him on the MPS albums Another Day, Walking the Line, In Tune (with the Singers Unlimited), and the retrospective The History of an Artist. Settling in New York, he joined the Thad Jones/Mel Lewis Orchestra and held the bass chair from 1973 to 1976, the Monday-night Village Vanguard band's most heavily recorded stretch, taking in Potpourri, Live in Tokyo, Suite for Pops, New Life, and the Meets Manuel De Sica project. He also became the bassist in Roland Hanna's New York Jazz Quartet when the group reorganised in 1974 around Hanna, Frank Wess, Mraz, and a rotating drum chair of Ben Riley, Richard Pratt, and Grady Tate, staying through Surge (1977), Song of the Black Knight (1978), Blues for Sarka (1978), Oasis (1981), and The New York Jazz Quartet in Chicago.

Through the second half of the 1970s he became one of the most requested bassists in New York, and no leader used him more consistently than Pepper Adams. Mraz played on six Adams leader dates across eight years: Ephemera (recorded September 10, 1973, at EMI Studios in London with Roland Hanna and Mel Lewis), the two albums drawn from a single live night at the Domicile in Munich on August 13, 1975, Julian and Twelfth & Pingree, both with Walter Norris and Makaya Ntshoko, and then three studio dates, Reflectory (1978, with Hanna and Billy Hart), The Master (1980, with Tommy Flanagan and Leroy Williams), and Urban Dreams (1981, with Jimmy Rowles and Hart). Reflectory and The Master both brought Adams Grammy nominations. The same years produced the three nights Art Pepper recorded at the Village Vanguard on July 28, 29, and 30, 1977, with George Cables on piano and Elvin Jones on drums, issued by Contemporary as Thursday Night, Friday Night, and Saturday Night at the Village Vanguard, plus steady work with Zoot Sims on Zoot Sims and the Gershwin Brothers (1975) and Warm Tenor (1979). He recorded three albums with Charles Mingus late in the bassist-composer's life, Three or Four Shades of Blues (1977), Me Myself an Eye (1979), and Something Like a Bird (1980), and was the original bassist in Quest, the group Dave Liebman and Richie Beirach formed at the end of 1981 with Al Foster on drums, playing on its self-titled first album before the rhythm section changed in 1984.

The partnership that came to define him lasted more than two decades. Mraz first recorded with pianist Tommy Flanagan on Eclypso, cut for Enja on February 4, 1977, with Elvin Jones, and stayed in Flanagan's trio through Ballads & Blues (1978), Plays the Music of Harold Arlen (1979), The Magnificent (1981), Confirmation (1982), Giant Steps (1982), Thelonica (1983), Nights at the Vanguard (1987), Jazz Poet (1989), Beyond the Bluebird (1991) with Kenny Burrell, and Elusive (1998). Alongside it he kept an unusually wide sideman book: Studio Trieste (1982) with Chet Baker and Jim Hall, Warne Marsh's Star Highs (1982) with Hank Jones and Mel Lewis, Stan Getz's Voyage (1986) and The Stockholm Concert (1989), Lee Konitz's Live at the Village Vanguard (1985), Carmen McRae's Carmen Sings Monk (1990), Gillespie's The Winter in Lisbon (1990), the Beirach-led Chet Baker tribute Some Other Time (1990) with Michael Brecker and John Scofield, Barry Harris trio dates from 1997 to 2000, Joe Henderson live sets across the 1990s, and the Herbie Hancock, Brecker, and Roy Hargrove Directions in Music tour of the early 2000s.

He waited an unusually long time to lead. Apart from a run of co-billed duo and trio records made for Japanese labels in the 1970s, the first album under his name alone was My Foolish Heart, cut June 11 and 12, 1995, for Milestone, and it opened a five-album run for the label: Jazz (1996), Bottom Lines (1997), Duke's Place (1999), and Morava (2001). The last of those turned him back toward home. Morava set Moravian folk songs for a quartet of Mraz, pianist Emil Viklický, singer and cimbalom player Zuzana Lapčíková, and drummer Billy Hart, and he pursued the idea for the rest of his life on Moravian Gems (2007) with Iva Bittová and Together Again (2014) with Viklický. He had already recorded Catching Up in Prague in October 1991, within two years of the Velvet Revolution, and he returned regularly for the Jazz at Prague Castle series, where a 2004 concert reunited him with Rudolf Dašek, the guitarist who had given him his first professional job nearly forty years earlier. The Czech Republic gave him a lifetime achievement award in 2009. He was treated for pancreatic cancer in 2016 and kept performing, latterly in a trio with his wife, pianist Camilla Mraz, and drummer Anthony Pinciotti. George Mraz passed away in Prague on September 16, 2021, one week after his seventy-seventh birthday.

Mraz built his reputation on things that are hard to show off with: intonation, time, and note choice. The conservatory years under František Hertl gave him a classical player's centred, singing tone and a bow technique few American jazz bassists could match, and he used arco for melody statements rather than as an effect, most audibly on the Moravian folk material he recorded with Emil Viklický. What leaders actually hired him for was the walking line. Jimmy Rowles nicknamed him "Bounce" for the lift he put under a rhythm section, and producer Todd Barkan described his note choices as so exact that each chorus works like a small piece of storytelling. That combination made him the house bassist for a particular kind of exacting pianist: Oscar Peterson, Roland Hanna, Hank Jones, Barry Harris, and above all Tommy Flanagan, all of whom kept him for years at a time. He was a sideman by temperament as much as by circumstance, taking twenty-seven years from his American debut to his first album under his own name, and the shape of his catalogue reflects it: of the 704 releases Discogs credits him on, only about 90 carry a leader or co-leader billing.