Jay Sawyer grew up in Grand Rapids, Michigan, and took his Bachelor of Music at Western Michigan University, where he played in the WMU Jazz Orchestra and Jazz Nonet under Trent Kynaston and Scott Cowan and toured with them to the Notre Dame, Elmhurst and Detroit jazz festivals. His drum teachers there were Tim Froncek and Keith Hall. He then went to the University of Illinois at Urbana-Champaign for a Master of Music, working as graduate assistant to drummer Dana Hall and playing alongside Chip McNeill, Chip Stephens, Jim Pugh, Tito Carrillo, Glenn Wilson and Ron Bridgewater. He also studied with Billy Hart. His earliest credited recording comes out of the Illinois years: saxophonist Rick Deja's self-released Itinerant, cut at Pogo Studio in Champaign and issued in 2013.

He moved to New York and turned up at Smalls for the first time on May 5, 2013, at an after-hours jam session. The clubs' archive tracks what happened next: more than 160 sets at Smalls, Mezzrow and Jazzcultural over the following thirteen years, over sixty of them with trombonist David Gibson's quartet, his longest-running standing gig since August 2019, vocalist Marianne Solivan, pianist Jason Yeager, baritone saxophonist Eden Bareket, and the Eyal Vilner Big Band, among others. Away from those rooms he has shared stages with Freddy Cole, John McNeil, Dee Dee Bridgewater, Stefon Harris, Donny McCaslin, Benito Gonzalez and Shai Maestro, and toured the United States and Europe, including the Montreal, Detroit and Chicago jazz festivals and the Festival Eclats d'Email in Limoges, France.

The association that has lasted longest on record is with Israeli trumpeter Itamar Borochov. It started on the bandstand, with the Itamar Borochov Quintet at Smalls on March 25, 2015, and Sawyer has held the drum chair on all three of Borochov's leader albums since: Boomerang (2016, Laborie Records), where the quartet was completed by Michael King on piano and Avri Borochov on double bass and oud; Blue Nights (2018, Laborie Records), with Avri Borochov still on bass and Rob Clearfield taking over the piano chair; and Arba (2023, Greenleaf Music), recorded over two days in April 2022 at Big Orange Sheep in Brooklyn with Clearfield and bassist Rick Rosato, produced by Matt Pierson with Dave Douglas as executive producer. He is credited on drums with no track restriction on all three, and adds percussion on Arba. He was also in the Borochov and Omer Avital band that played Smalls in August and December 2025.

Three other working relationships run in parallel. He is the drummer on both of alto saxophonist Caroline Davis's Sunnyside albums of the period, Heart Tonic (2018) and Anthems (2019), the second of them credited to Caroline Davis & Rob Clearfield's Persona and recorded in a single day at Acoustic Recording in Brooklyn in February 2018. He has held the chair in violinist Tomoko Omura's Branches project across Branches Vol. 1 (2020), Branches Vol. 2 (2021) and Run Run Run (2025) on Outside In Music, a band completed by Glenn Zaleski on piano, Jeff Miles on guitar and Pablo Menares on bass. And he has recorded three times with pianist Jason Yeager, including the septet date Unstuck In Time: The Kurt Vonnegut Suite (2022, Sunnyside), which carries Miguel Zenón as special guest.

His only release billed under his own name is a co-operative one. Anchor Points (OA2 Records, October 2023) puts no leader on the sleeve, just the names of pianist Russell Kranes, guitarist Alex Levine, bassist Sam Weber and Sawyer, four players who had been working together on the New York scene for about a decade. It was taped at Benny's Wash & Dry in Brooklyn on February 18 and 19, 2022, and splits itself in two: Sawyer plays on four of the eight tracks, and the other four are a drummerless trio. He has since begun leading his own trio, taking it into Smalls on July 14, 2026. Alongside the playing he teaches privately and in workshops, master classes and ensemble settings, with students ranging from three years old to eighty-three.

Sawyer is a colorist first, and the reviews of his work keep returning to how much detail he gets out of quiet playing. Ian Mann, writing in The Jazz Mann about Arba, described "crisp but sensitive cymbal embellishments," a drummer "impressing with the subtlety and detail of his playing," mallet rumbles and cymbal shimmers under a Borochov solo, and stretches of hand drumming used in place of sticks, all on a record that also has him "drumming up a storm." Lucid Culture heard the same range in Tomoko Omura's band: a "dubwise pulse" with guitarist Jeff Miles on Branches Vol. 1 and "whispery brushwork" behind a bass solo on Branches Vol. 2. OA2 Records, introducing Anchor Points, reached for the opposite end of him and called it "jubilant swing." That span is what makes him useful across catalogs as unalike as Borochov's quarter-tone maqam settings, Omura's Japanese-folk arrangements for violin and guitar, Caroline Davis's electronics-shaded quartets and Ian Hutchison's straight bebop repertoire record. His lineage runs through his teachers: Tim Froncek and Keith Hall at Western Michigan, Dana Hall at Illinois, where he was Hall's graduate assistant, and Billy Hart.