Murphy was born in Carbonear, Newfoundland, 105 kilometres west of St. John's, and is the second of five children of Harry and Marie Murphy. He graduated from Memorial University of Newfoundland in 1968, and went to the United Kingdom to study at St Edmund Hall in the University of Oxford as a Rhodes scholar. He did not receive an Oxford degree.
Murphy first came to national attention while attending Memorial University during a nationally covered speech in Lennoxville, Quebec. Murphy characterized Newfoundland Premier Joey Smallwood's governing style as dictatorial and proclaimed his legislature's recent announcement of free tuition as a sham. Smallwood warned the undergraduate student in a news conference not to return. Murphy did and was elected President of Memorial University Student Council. In the end the government caved in. All students received the free tuition promised, plus a $50 living allowance.
Murphy has run for provincial office in Newfoundland twice: in the 1985 provincial election in the riding of Placentia in 1985 and in a byelection in the riding of St. John's East in 1986, as a Liberal. He lost both times. He also worked in the 1980s as executive assistant to Clyde Wells.
Murphy is a frequent presence on the various branches of the CBC. He has regular commentary segments entitled "Point of View" on The National, the CBC's flagship nightly news program. He was the regular host of CBC Radio One's Cross Country Checkup, a nationwide call-in show.
He also wrote a column for the Saturday edition of the Globe and Mail newspaper until January 2010, when the Globe cancelled the column and Murphy moved to the National Post. Murphy's writing is characterized by a polysyllabic style and a wide range of cultural references.
He is a vocal critic of arguments for anthropogenic climate change and proposed policy responses for it, such as the Green Shift.
In 2004, he and nine other prominent Canadians participated in the production and the defence of a Great Canadian on the CBC Television program The Greatest Canadian. Murphy, advocating for former prime minister Pierre Trudeau, guided his candidate to third place in the final vote.
Murphy announced in September 2015 that he will retire from Cross Country Checkup as of September 20, while he will continue his weekly commentary segment on The National.
In June 2008, Murphy was awarded an Honorary Doctor of Laws degree from the University of Waterloo. He was awarded honorary doctorates of letters by Memorial, St. Thomas, and Nipissing universities. In June 2013, he was awarded the Honorary Fellowship of the Canadian Institute of Management.
After receiving several public complaints in 2014, the CBC's ombudsman investigated claims that Murphy may have been in conflict of interest by criticizing opponents of the Alberta oil sands in his Point of view segments while receiving money from the oil industry for paid speeches on at least 25 separate occasions. In the final report and subsequent to an investigation, the CBC's ombudsman, Esther Enkin, concluded that Murphy's speeches to certain companies in the oil industry while working for the CBC did present "an apparent conflict of interest". In light of these events, the CBC reviewed its standards and practices for its journalists and employees with regards to paid speeches.