Between 1989 and 1997, he was a Sinn Féin councillor on Newry and Mourne District Council for The Fews area, in South Armagh and South Down, and served as his party's group leader at that level.
In 2011, while Minister for Regional Development, Murphy appointed Seán Hogan, a Catholic, as head of Northern Ireland Water, turning down the applications of four Protestants on the shortlist. A tribunal subsequently awarded £150,000 damages for discrimination to one of these applicants, Alan Lennon, judging that Hogan was appointed because "he was not from a Protestant background and because he was known to the minister and his ministerial colleagues Michelle Gildernew and Caitríona Ruane, who were consulted about the appointment." The tribunal found Murphy's evidence was "implausible and lack credibility", and that, during Murphy's tenure at the Department for Regional Development, there was a "material bias against the appointment of candidates from a Protestant background". Murphy disputed the finding which he said branded him "sectarian". Deputy First Minister of Northern IrelandMartin McGuinness defended him, claiming Murphy doesn't have "a sectarian bone in his body".
Witness in Declan Gormley case
In December 2012, Murphy appeared as a witness at Belfast High Court in the case of Declan Gormley, whom Murphy had sacked in 2010 from his post as a non-executive director of NI Water. Gormley sued Sinn Féin over two press releases which he argued were defamatory. Gormley was subsequently offered £80,000 in damages.
Controversy over comments about Paul Quinn
In 2007, shortly after the murder of Paul Quinn, Conor Murphy said in an interview with Spotlight that "Paul Quinn was involved with smuggling and criminality and I think that everyone accepts that." During the 2020 Irish general election Conor Murphys' comments were an issue. Breege Quinn said that her son was definitely not involved in criminality and called on Conor Murphy to withdraw his remarks and make a public apology to the Quinn family. On 6 February 2020 Conor Murphy spoke to RTÉ and said that he had withdrawn the remarks he had made in 2007 and apologised to the Quinn family. Breege Quinn repeated her call for him to resign as Minister for Finance at Stormont. She said he "should finish off and get justice" for the Quinn family. She said he should "go and tell the PSNI and the Gardaí exactly who he was speaking to" in the IRA after the murder. She said she would not meet Conor Murphy until he "comes out publicly saying that he is going to the PSNI to give the names of the IRA that he spoke to in Cullyhanna".