Murphy earned a Bachelor of Science in chemical engineering from Cornell University, summa cum laude, in 1999, a Master of Science and Doctor of Philosophy in chemical engineering from the California Institute of Technology in 2002 and 2004, and a Juris Doctor from Harvard Law School, cum laude, in 2007.

[3] From 2008 to 2009, Murphy served as a law clerk for Judge Kimberly A. Moore of the United States Court of Appeals for the Federal Circuit.

[3] In 2019, Murphy represented a number of plaintiffs suing to block the Pennsylvania Secretary of State's certification of ExpressVote XL electronic voting machines, challenging the security, reliability, and accuracy of the machines.

Murphy had been recommended by Senator Patrick Toomey and was nominated as part of a bipartisan package of nominees which included Kelley B. Hodge, Kai Scott, and Mia Roberts Perez.

[10] President Biden nominated Murphy to the seat vacated by Judge Lawrence F. Stengel, who retired on August 31, 2018.