Mance was born on 6 June 1943, one of four children of Sir Henry Stenhouse Mance, one-time chairman of Lloyd's of London.
Like his father, he attended Charterhouse School, a boarding school in Godalming, Surrey. He then studied at University College, Oxford, and was called to the Bar by the Middle Temple in 1965, becoming a QC in 1982 and a Bencher in 1989.
In 1990, he became a recorder, and on 25 October 1993 was appointed a High Court judge, serving in the Queen's Bench Division, and received the customary knighthood. On 27 April 1999, he was appointed a Lord Justice of Appeal, and appointed to the Privy Council.
On 3 October 2005, he was appointed a Lord of Appeal in Ordinary as Baron Mance, of Frognal in the London Borough of Camden. He was introduced in the House of Lords on 12 October 2005. On 1 October 2009, he and nine other Lords of Appeal became Justices of the Supreme Court upon that body's inauguration. In a speech to the Hoge Raad in The Netherlands in 2013, Lord Mance described the creation of the Supreme Court as the consequence of a "back of an envelope plan".
He has also served as Chairman of the Banking Appeals Tribunal (1992–93), Chairman of the Consultative Council of European Judges (2000), President of the British Insurance Law Association (2000–02), and trustee of the European Law Academy (2003).
Mance was appointed Deputy President of the Supreme Court of the United Kingdom in September 2017, succeeding Baroness Hale who becomes President of the Supreme Court. He will be sworn into the new position on 2 October 2017.
In October 2012, the Chancellor of the University of Oxford, the Lord Patten of Barnes, appointed Lord Mance as High Steward of the University of Oxford, on the retirement of Lord Brown of Eaton-under-Heywood. He is an honorary fellow of University College, and Visitor of St Cross College, Oxford. In 2013 He received an honorary doctorate from Canterbury Christ Church University.The Public Prosecution Service v William Elliott, Robert McKee  UKSC 32
He is married to Dame Mary Arden, currently a Lord Justice of Appeal; the two are the first married couple ever to serve concurrently in the Court of Appeal. They have two daughters and a son together. His recreations include tennis, languages, and music.