Murphy played high school basketball at St. Mark's School in Southborough, Massachusetts.
Considered a four-star recruit by Rivals.com, Murphy was listed as the No. 22 power forward and the No. 79 player in the nation in 2009.
Murphy accepted an athletic scholarship to attend the University of Florida in Gainesville, Florida, where he played for coach Billy Donovan's Florida Gators men's basketball team from 2009 to 2013.
Murphy became the 49th Florida Gator to record 1,000 points in his collegiate career and was the only Gator to receive first-team all-conference accolades in 2013. He proceeded to become a regular in the starting lineup in his junior year, and was named to the All-SEC Tournament team in 2012 and 2013.
Murphy was selected with the 49th overall pick by the Chicago Bulls in the 2013 NBA draft. On July 10, 2013, he signed his rookie scale contract with the Bulls. On November 6, 2013, Murphy made his NBA debut for the Bulls, playing one minute and not recording any stats. He scored a career-high 2 points on three different occasions: December 10, 2013 vs. Milwaukee, December 28, 2013 vs. Dallas, and March 13, 2014 vs. Houston. On April 3, 2014, he was waived by the Bulls. On April 5, 2014, he was claimed off waivers by the Utah Jazz.
On July 22, 2014, Murphy was traded, along with John Lucas III and Malcolm Thomas, to the Cleveland Cavaliers in exchange for Carrick Felix, a 2015 second round draft pick and cash considerations. On September 25, 2014, he was traded, along with John Lucas III, Dwight Powell, Malcolm Thomas and the Cavaliers' 2016 and 2017 second-round picks, to the Boston Celtics in exchange for Keith Bogans and two future second-round picks. On October 27, 2014, he was waived by the Celtics.
On November 1, 2014, Murphy was selected by the Austin Spurs with the third overall pick in the 2014 NBA D-League draft.
On July 4, 2015, Murphy signed with Beşiktaş of the Turkish Basketball Super League for the 2015–16 season. In late December 2015, he left Beşiktaş. On January 4, 2016, he signed with Demir İnşaat Büyükçekmece for the rest of the season.
On June 26, 2016, Murphy signed with Strasbourg IG of the LNB Pro A for the 2016–17 season. He will join Finnish national coach Henrik Dettman who reached an agreement with the Strasbourg IG earlier.
On July 28, 2017, Murphy signed with Nanterre 92 for the 2017–18 season.
Murphy made his debut for the Finnish national team in August 2014 in a friendly match against Lithuania. He recorded nine points and five rebounds in his debut appearance. He later played in the 2014 FIBA Basketball World Cup where Finland's campaign was ended at the group stages; Murphy averaged 6.8 points over five games. He represented Finland again at EuroBasket 2015, helping his team advance out of the group stage.
Murphy's father, Jay Murphy, is a former NBA player while his mother, Päivi, played for the Finland women's national basketball team from 1988–1994. His younger brother Alex Murphy plays at Florida.
He holds both American and Finnish passports.