Joe Strasser grew up in Bethel, Connecticut, and moved to New York City in 1990, at nineteen, to study at the New School's jazz program. He has described it as an apprenticeship rather than a lecture hall: roughly 120 students, with the faculty available to play alongside. No birth date has been published for him, and nothing in print documents his playing before he arrived in New York, so his training prior to 1990 is not confirmed.

He landed in the basement club that defined his generation of New York players. Bassist Omer Avital built a piano-less, saxophone-heavy band at Smalls in the mid-1990s, and Strasser held the drum chair in one of its lineups. A set the band played there in early 1997 sat on the shelf for a decade before Smalls Records issued it in 2007 as Room To Grow (SRCD-0020), with Strasser behind Charles Owens, Grant Stewart and Greg Tardy on tenors and Myron Walden on alto. The release itself carries the recording note: "Recorded in early 1997 live at Smalls, NYC." The album is often filed as a 2007 session, which is a decade off. That summer, on July 3 through 6, 1997, Impulse! recorded four nights at the club for Jazz Underground: Live at Smalls, released in 1998, and Strasser is one of four drummers credited on it. The Avital Group takes two of the record's nine tracks, "Kentucky Girl" and "I've Never Been In Love Before," though the release does not break its drum credits out by track.

Through the 2000s his name became a fixture on Marc Edelman's Sharp Nine label. He co-founded the Hotpants, a funk band that held a long run at Smoke, with alto saxophonist Ian Hendrickson-Smith, and he was the drummer on both of Hendrickson-Smith's Smoke live dates for Sharp Nine: Up In Smoke (recorded September 22 and 23, 2002, released 2003) with Barak Mori on bass and David Hazeltine on piano, and Still Smokin' (recorded January 9 and 10, 2004) with Peter Washington, Peter Bernstein, Hazeltine and Ryan Kisor. He was also the drummer in Planet Jazz, the sextet founded by the late Johnny Ellis and later led by pianist Spike Wilner. Planet Jazz cut In Orbit at Systems Two in Brooklyn on December 19, 2005, then returned with a club album, Live At Smalls (SmallsLIVE SL-0011, 2010), where Jerry Weldon took the tenor chair opposite Joe Magnarelli, Bernstein, Wilner and Neal Miner. Other work from these years ran through Nagel Heyer (Champagne Taste, cut live at Smoke in May and June 2002 with Jim Rotondi's Full House, and trombonist David Gibson's The Path To Delphi, November 21, 2004, with Randy Brecker) and Fresh Sound New Talent (Wilner's Late Night: Live At Smalls, from sets in November 2002 and January 2003). He also kept a chair in Charles Owens's Friday late-night quartet at Smalls in 2003. Owens taped those sets on two ceiling microphones and released them 23 years later, in May 2026, as The Last Late Nights; Strasser drums on the April 25 and May 16 sessions.

From the 2010s on he settled into a rhythm-section role that European and American labels both kept calling. He is the drummer in alto saxophonist Dmitry Baevsky's trio and quartet records, sharing the billing on Over And Out (with bassist David Wong) and returning for Somethin' Special (Blau, 2016). Posi-Tone made him a house drummer of sorts: Ken Fowser's Don't Look Down (2018) and Morning Light (2020), the collective quintet Works For Me on Reach Within (recorded June 6, 2019), Farnell Newton's Feel The Love (2021), and the Charles Mingus repertory group Blue Moods on Myth & Wisdom (recorded June 4 and 5, 2021). He also took the drum chair in Peter Leitch's New Life Orchestra for its double album New Life, recorded in Mount Vernon, New York on January 17 and 18, 2020. Away from the clubs he turns up on Kyle Eastwood's Time Pieces (Jazz Village, 2015) and on the soundtrack to the film Maggie's Plan (2016), sharing the drum credit on both. Published bios list George Coleman, Harold Mabern, Etta Jones, Cecil Payne, Jane Monheit and Hillary Kole among the leaders he has worked for; none of those associations has been traced to a specific release.

In 2026 he became a club owner. One Flight Up, at 108 Greenwich Street in the Financial District, opened quietly that summer with Strasser as co-owner alongside the lawyer Mark Quinn, a friend since the 1990s Greenwich Village club circuit. Strasser funded his share partly with money left by his father, a jazz fan who had asked him before his death whether he wanted a room of his own. The name comes from the Dexter Gordon album, and the club is also literally one flight up. Darcy Burke, formerly the manager of Smalls, runs the room day to day, and Strasser still plays in it. He remains a working drummer at Smalls and Mezzrow, and a quintet date billed to Spike Wilner with Baevsky, guitarist Yves Brouqui, bassist Paul Gill and Strasser, Bird's Words, is scheduled for release on SteepleChase (SCCD 34020) on September 18, 2026.

Strasser's sound starts at the ride cymbal, and both of his longest-running employers say so in nearly the same words. "The second he hits the cymbal, you know who it is," Ian Hendrickson-Smith told All About Jazz in 2007, calling the beat "really crisp and exact." Spike Wilner traced the lineage: Jimmy Cobb first, then Philly Joe Jones and the classic bebop drummers. Writing about three Sharp Nine records, David A. Orthmann described a colorist who keeps the cymbal light enough to push a band without crowding it, tunes his tom-toms for a bell-like clarity, and uses the bass drum sparingly enough that each hit registers, including comping figures most drummers would put on the snare. His solos drew the strongest reaction from his peers. Wilner called them "really quite unusual," and pointed to the eight-bar break Strasser devised for "Mommy, Mommy NO!" on In Orbit, a five-note figure played in unison on bass drum and cymbal that turns out to be built from the tune's melody. Orthmann's summary of his standing is worth keeping as written: you will search in vain for his name in critic and listener polls.