Justice McEvoy began his legal career as Associate to the then Chief Justice of the Federal Court in 1994, and was admitted as a Barrister and Solicitor of the Supreme Court of Victoria and the High Court of Australia in 1996. He was subsequently a solicitor and then senior associate in the litigation and competition groups at Freehills (now Herbert Smith Freehills) in Melbourne and Sydney. He practised at the Victorian Bar from 2002 until 2019, largely in general commercial, public, and common law. He was appointed Senior Counsel in Victoria in 2016. In 2019 his Honour was appointed to the Family Court of Australia, and in 2020 he was appointed as a judicial Deputy President of the Administrative Appeals Tribunal.

Immediately prior to his appointment to the Family Court, Justice McEvoy was Senior Counsel Assisting the Royal Commission into Aged Care Quality and Safety. His Honour has been a member of the Visiting Faculty at the University of Virginia School of Law since 2001, teaching an annual course in the conflict of laws. He has been a Fulbright Scholar, and has served as a member of the Australian delegation of experts to a special commission of The Hague Conference on Private International Law (Jurisdiction and Judgments Convention). In 2018 he was elected to the American Law Institute. His Honour has published a number of articles on private international law, administrative law, and competition law in Australian and international law journals. He is a Board Member of OzChild.