Squyres has had an extended collaboration with the Taiwanese director Ang Lee, having edited all but one of Lee's feature films.

Squyres was born in Wenonah, New Jersey. He is the brother of Steve Squyres, professor of astronomy at Cornell University. Both brothers attended Cornell after attending Gateway Regional High School in New Jersey.

Squyres has edited all of Ang Lee's films except for Brokeback Mountain, including The Wedding Banquet (1993), Eat Drink Man Woman (1994), Sense and Sensibility (1995), Ride with the Devil (1999), Crouching Tiger, Hidden Dragon (2000), The Hire: Chosen (2001), Hulk (2003), Lust, Caution (2007), Taking Woodstock (2009), and, most recently, Life of Pi (2012).

Squyres' work on Crouching Tiger, Hidden Dragon (2000) earned nominations for the Academy Award for Best Film Editing, the BAFTA Award for Best Editing, the American Cinema Editors Eddie Award, among other awards. His work on Gosford Park (directed by Robert Altman - 2001) was also nominated for an Eddie.

In 2012, he was also nominated for the Academy Award for Life of Pi.

Squyres has been elected to membership in the American Cinema Editors

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