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Born of Polish parents, Mink was raised in Toronto, Ontario. He got his start performing with the rock/country group Mary-Lou Horner, which became the house band at "The Rockpile" bar and nightclub. They opened for Led Zeppelin and Muddy Waters, along with being a backup band for Chuck Berry.
Mink is best known as a long-time collaborator with Canadian singer k.d. lang, whom he met at Expo '85 while doing a gig with CANO. Mink has performed on, along with co-writing and producing several of her albums, which often combine voice with string arrangements. Mink subsequently performed as violinist, guitarist, and mandolinist with lang's band, the Reclines. A performance was recorded as part of the MTV Unplugged series at the Ed Sullivan Theater, New York City, December 16, 1992 (aired in 1993).
Additionally, Mink was invited to play electric violin on the Rush song "Losing It" from the band's 1982 album Signals and contributing strings to the song "Faithless" from the 2007 album Snakes & Arrows. He also performed guitar parts on My Favourite Headache (2000), a solo project of Rush's lead singer Geddy Lee.
Mink has also produced and/or performed on recordings by numerous other artists, a diverse group which includes the Barenaked Ladies, Meryn Cadell, Marie-Lynn Hammond, Dan Hill, Mendelson Joe, Prairie Oyster, Raffi (musician), Jane Siberry, Sylvia Tyson, Valdy, Bruce Cockburn, Murray McLauchlan, Willie P. Bennett, Susan Aglukark, and Ann Wilson of Heart.
Mink was also responsible for the movie soundtrack to Fifty Dead Men Walking. which has since received numerous awards and nominations including a 2010 Genie Award nomination for Best Achievement in Music – Original Score, and a 2009 Leo Award for Best Musical Score for a Feature Length Drama. The television soundtracks for Terminal City. and Alice (TV miniseries)., both garnered Leo Awards. Confessions of an Innocent Man, a shocking, heart-wrenching story about British-Canadian engineer William Sampson (author), won a 2007 Gemini Award for Best Biography Documentary Program.
He co-produced Red Velvet Car with Ann and Nancy Wilson, the newest album by Heart released in the fall of 2010  and appears onstage in the band's concert video Night At Sky Church. Mink was back at the helm as producer of Heart's upcoming album 'Fanatic'.
Mink has lectured on such topics as “The Music Business vs. the Creative Process,” at the University of British Columbia, University of Western Washington and Simon Fraser University. He has also worked with students as an associate of UBC’s Department of Mechanical Engineering (robotics) and is an associate member of the Institute for Computing, Information & Cognitive Systems. In 2006 Mink delivered the introductory speech for k.d. lang’s Governor General’s Performing Arts Award induction at the National Arts Centre in Ottawa. He has also contributed to the Library and Archives Canada 
Mink is a member of the Black Sea Station, a North American klezmer supergroup. Their debut recording, Transylvania Avenue, is produced by Mink, and was released on Rounder Records in the Fall of 2010 as a digital download. He's also produced other klezmer musical acts in the past such as Finjan, The Klezmatics and Chava Alberstein.
Mink is one of only a few people to ever share a songwriting credit with Mick Jagger and Keith Richards. In 1997 Mink and k.d. lang were co-credited as songwriters on the Rolling Stones single "Anybody Seen My Baby?". Mink and Lang were given credit before the song was released because Jagger/Richards felt the chorus was very similar to "Constant Craving", written by lang and Mink in 1992.
In 1990, Mink was co-nominated with Lang for a Best Country Song Grammy for "Luck in My Eyes". In 1993, he and Lang won a Juno Award for Best Songwriter of the Year. Continuing his partnership with Lang, a year later the pair won another Juno for Producer of the Year for the song "Just Keep Me Moving" on Even Cowgirls Get the Blues.