The third son of Robert (a barrister) and Jane Miller, Maxwell Miller attended St Paul's School for nine years before winning the Camden exhibition scholarship to Worcester College, Oxford, in 1850. He transferred as a Fitzgerald scholar to Queen's College in 1851 but left without finishing his degree. At twenty, he migrated to Australia and worked as an inspector of Anglican schools in Melbourne at the request of Bishop Perry. He then undertook a career in journalism, becoming sub-editor of the Argus. A commitment to educational improvement, however, remained his major concern. Miller arrived in Hobart in 1855 at the invitation of his brother William to help establish the Tasmanian Daily News (1855-1858), which later merged with The Mercury. Elected to the House of Assembly in 1856, he vigorously pursued his endeavours for educational reform, advocating support for a bill proposed by Premier Francis Smith for creating a Tasmanian Council of Education which was eventually passed in 1858. Miller resigned soon after publishing a book of satirical verses, The Tasmanian House of Assembly: A Metrical Catalogue, in 1860. Re-elected as the MHA for Hobart in May 1862, Miller again resigned in 1864, taking up an appointment as assistant clerk and librarian to Parliament.
Ferguson's Bibliography of Australia includes Miller's Financial Condition of Tasmania, a speech delivered before a public meeting at the Hobart Town Mechanics' Institute on 27 January 1862 and published by request, in addition to his Catalogue of the Blue Books in the Possession of the Parliament of Tasmania, 1st May, 1865.