Joseph Allen Farnsworth was born on February 21, 1968, in South Hadley, Massachusetts, the youngest of five sons of Roger Farnsworth, a music teacher, trumpeter and bandleader who raised his children on jazz. His brother John became a professional jazz saxophonist, and his brother James played baritone saxophone in Ray Charles's band from 1992 until his death in 1999. After South Hadley High School he went to William Paterson College in New Jersey, where he studied with the pianist Harold Mabern and the drummers Art Taylor and Alan Dawson and took a bachelor of music degree in 1990. By his own account he met Mabern there in 1986 and the tenor saxophonist Eric Alexander in 1987, and the three formed a working relationship that lasted for decades.

He moved to New York City in the early 1990s and was soon working with the tenor saxophonist Junior Cook, the singer Jon Hendricks, the trumpeter Jon Faddis, George Coleman and the baritone saxophonist Cecil Payne. He is on Payne's comeback record Cerupa, cut in Chicago on June 1 and 2, 1993, for Delmark. That same year he took over the Friday and Saturday drum chair at Augie's, a bar on Broadway on the Upper West Side, and he says he used the job to bring in older players including Cook, the bassist John Ore, Payne, the organist Big John Patton, the trumpeter Dizzy Reece, the trombonist Julian Priester and Mabern. When the room reopened as Smoke in April 1999 under Paul Stache and Frank Christopher, he played the first weekend and, as he tells it, talked Stache into booking Coleman and Mabern. He calls the club a second home, and he has recorded for its Smoke Sessions label.

In 1995 he became a founding member of One for All, the hard-bop sextet formed with Alexander, the trumpeter Jim Rotondi, the pianist David Hazeltine, the trombonist Steve Davis and the bassist Peter Washington, with John Webber taking the bass chair later. The group's records include Too Soon to Tell (Sharp Nine, 1997) and Upward and Onward (Criss Cross, 1999). In the second half of the 1990s he also recorded with Steve Davis, with Benny Golson (Tenor Legacy and Remembering Clifford), with the pianist Michael Weiss and in the Three Baritone Saxophone Band, and he worked with Benny Green, the singer Annie Ross and, in 1999 and 2000, Diana Krall. His first record as a leader, Beautiful Friendship (Criss Cross, 1999), is a sextet date with Cedar Walton, Eddie Henderson, Alexander, Davis and the bassist Nat Reeves.

He says he spent about sixteen years, from roughly 2000 to 2016, in Pharoah Sanders's band, a job that came on Coleman's recommendation, and he is the drummer on Sanders's Venus date The Creator Has a Master Plan (2003). He also recorded the live album Live at the House of Tribes with Wynton Marsalis, made a series of trio albums with Mabern, and later played in McCoy Tyner's group during the last part of Tyner's life. His own records in this period, several of them made for Japanese labels, were built around a recurring band of Alexander, Mabern, Hazeltine, Rotondi, Reeves and the trombonist Curtis Fuller: It's Prime Time (Eighty-Eight's, recorded January 30, 2003, with Ron Carter and Golson added), Drumspeak (Commodore, 2006), Super Prime Time (Eighty-Eight's, 2012) and My Heroes (Venus, 2014).

From 2020 his leader albums have come out on Smoke Sessions. Time to Swing was recorded live in the studio on December 17, 2019, with Kenny Barron and Washington and with Marsalis on four tracks, and was released on September 16, 2020. City of Sounds (2021) is a trio date with Barron and Washington recorded at Smoke in February 2021. In What Direction Are You Headed? (2023) turned to a younger band with Immanuel Wilkins, Kurt Rosenwinkel, the pianist Julius Rodriguez and the bassist Robert Hurst. The Big Room, recorded at a daytime session at Smoke on January 23, 2025, and released on July 25, 2025, pairs him with the trumpeter Jeremy Pelt, the alto saxophonist Sarah Hanahan, the vibraphonist Joel Ross, the pianist Emmet Cohen and the bassist Yasushi Nakamura; it spent a week at number one on the JazzWeek radio chart.

Farnsworth is a straight-ahead swing drummer from the hard-bop lineage, and nearly all of his work is as a rhythm-section player for horn and piano soloists in the Mabern, Cedar Walton and George Coleman tradition. His teachers were Art Taylor and Alan Dawson, and the musicians he credits with shaping him are the older players he worked for, among them Mabern, Coleman, Cook, Cecil Payne, Pharoah Sanders and McCoy Tyner. His website describes his playing as fast, precise, musical and melodic, and it quotes Sanders calling him a great person and a great player. As a leader he has favored a multi-horn front line, first in the Prime Time band of tenor saxophone, trumpet, trombone and piano and more recently in an intergenerational sextet, and he has said that he planned Time to Swing like an old record date, a trio side followed by a side with Wynton Marsalis. Reviews quoted on his website place The Big Room among the best jazz albums of 2025, and Modern Drummer is quoted there calling it his best record as a bandleader.