Maxwell was educated at Melbourne Grammar School, and proceeded to the University of Melbourne where he was resident at Trinity College. He played rugby and Australian Rules football at Trinity, where he was the Senior Student in 1973. After graduating he was selected as Victorian Rhodes Scholar for 1975, completing a BPhil at Oxford. He was then called to the Bar as a member of Lincoln's Inn in 1978, practising briefly at the English Bar before returning to Melbourne in 1979. From 1983 he was variously reader for Kenneth Hayne QC, Principal Private Secretary to Gareth Evans (Commonwealth Attorney-General), and reader for Ross Robson QC. He signed the Victorian Bar Roll in 1984 and became a QC in 1998.
Maxwell was the Victorian Legal Aid Commissioner for seven years and also a member of the Board of Liberty Victoria for six years, two of them as President. He appeared with Julian Burnside QC in the Tampa refugee case, and was then famously but unsuccessfully countersued (as a Board member of Liberty Victoria) by the Commonwealth of Australia for costs. In 1982 he published An Introduction to the Securities Industry Codes (Sydney: Butterworths, 1982) with Robert Baxt and Selwyn Bajada, released in a second edition in 1988 as Stock Markets and the Securities industry: Law and Practice (Sydney: Butterworths, 1988). He was later commissioned by the Victorian government to review the Occupational Health and Safety Act 1985.