Although he comes from several generations of bassists, he was not encouraged by them to go into music. In an interview with ActiveBass magazine he said that he has no contact with the professional bassists in his family.
His major teachers include Herman Reinshagen and Stuart Sankey, with whom he studied at the Aspen Music Festival and the Juilliard School. Karr's breakthrough came in 1962, when he was featured as a soloist in a nationally televised New York Philharmonic Young People's Concert, conducted by Leonard Bernstein. On that famous telecast, Karr performed "The Swan" from The Carnival of the Animals by Camille Saint-Saëns. Karr also recorded the piece with Bernstein and the New York Philharmonic.
He has since appeared as a soloist with the Chicago Symphony Orchestra, London Symphony Orchestra, London Philharmonic Orchestra, Montreal Symphony Orchestra, Hong Kong Philharmonic, Simon Bolivar Orchestra, Jerusalem Symphony, Oslo Philharmonic, Zurich Chamber Orchestra, and with all the major orchestras of Australia.
He has premiered new works written for him by Vittorio Giannini (Psalm CXX), Alec Wilder (Sonata for Double Bass and Piano and Suite for Double Bass and Guitar), Robert Xavier Rodriguez (Ursa, Four Seasons for Double Bass and Orchestra), and the concertos for double bass and orchestra by Gunther Schuller, Hans Werner Henze, John Downey and Ketil Hvoslef. He has recorded the Serge Koussevitzky concerto with Oslo Philharmonic.
He has taught double bass on the faculties of the Juilliard School, New England Conservatory of Music, The Hartt School, Yale University, Indiana University, University of North Carolina School of the Arts, and the Halifax (Nova Scotia) Schools Music Program and has published a number of instructional books for the double bass. He focuses on finding one's unique sound on the double bass and approaching playing with the lyrical emphasis of a singer.
After 40 years as a concert artist he retired in 2001 to Victoria, British Columbia, where he lives with his dog Shin-Ju.
In 1967 Karr founded the International Society of Bassists (ISB), an organization devoted to the study, promotion, and advancement of double bass playing around the world. The ISB, with a membership of more than 3,000 double bass performers, teachers, students, and aficionados in more than 40 countries, hosts an international conference biannually to further these goals.
Karr was featured in a documentary, The Great Double Bass Race, which was released in association with BBC Television in 1978.
In 2005, Karr donated his primary instrument, the Karr-Koussevitzky bass, to the ISB. This instrument was given to Karr by Olga Koussevitzky, widow of Serge Koussevitzky, in 1961. It is the intention of the ISB to make this valuable instrument available for use by double bassists worldwide. The Karr-Koussevitzky bass was once believed to have been made by the Amati family and hence it is also referred to as the Amati bass.
The non-profit Karr Double Bass Foundation, which loans instruments to promising young double bassists to assist in their professional development, was established by Karr in 1984.