[3] With Motherwell having qualified for European competition, in July 2008 Murphy scored a hat-trick against Albanian side Flamurtari in the UEFA Europa League.

[14] Despite interest from Huddersfield Town and Rangers, Murphy's move to Sheffield United was finalised on 3 January 2013, when he signed a three-and-a-half-year contract for an undisclosed fee.

[15] Murphy made his Blades debut two days later, in a 3–0 third round FA Cup victory against Oxford United at the Kassam Stadium,[16] Before making his league debut for United against Yeovil Town at Bramall Lane a week later,[17] and Murphy's first goal for the Blades came in a 2–0 away victory against Bury the following February.

[23] Later that day, Murphy came off the bench in the second half and scored a brace against promotion rivals Swindon Town to give United a 2–0 home victory.

[26] Murphy scored his first goal for Brighton on 26 September, in a 2–2 draw with Bolton Wanderers that also saw him receive a red card in the second half of the game.

[30] On 6 January 2018, Brighton announced that Murphy had joined Scottish Premiership club Rangers on loan until the end of the 2017–18 season.

[33] He suffered an anterior cruciate ligament injury in August 2018 whilst playing an away fixture on the artificial turf at Kilmarnock, which ruled him for most of the 2018–19 season.

[35] On 29 August 2020, Murphy signed for fellow Scottish side Hibernian on an initial one-year loan, with an obligation of a further year on a permanent basis.

[36][37] On 29 July 2021, Murphy scored his first goal for Hibernian in Europe against FC Santa Coloma in a 2–1 away win in the UEFA Conference League qualifiers.

[45] Murphy made his full international debut in a 1–0 home friendly defeat to Costa Rica on 23 March 2018, coming on as an 87th-minute substitute for Matt Ritchie.