Mingos undertook postdoctoral research at Northwestern University (Fulbright Fellow 1968–70) and at the University of Sussex (ICI Fellow 1970–71). From 1971 until 1976 he was a Lecturer at Queen Mary, University of London. He then moved to the University of Oxford as Fellow and Tutor at Keble College and University Lecturer. From 1977 until 1992 he was also Lecturer at Pembroke College, Oxford.
In 1978, Mingos, Stephen G. Davies and Malcolm Green compiled a set of rules that summarise where nucleophilic additions will occur on pi ligands.
Mingos 1984 paper on the polyhedral skeletal electron pair theory develops Wades electron counting rules for predicting the molecular geometry of cluster compounds.
In 1990 he was appointed Reader in Inorganic Chemistry and for the academic year 1991/92 he served as Assessor. From 1992 until 1999 he worked at Imperial College London as Sir Edward Frankland British Petroleum Professor of Inorganic Chemistry (1992–99) and Dean of the Royal College of Science (1996–99).
In 1999 Mingos was appointed Principal of St Edmund Hall, Oxford and at the same time he became a visiting professor at Imperial College London. In 2000 he received as a Title of Distinction the title of professor of inorganic chemistry at the University of Oxford. He was superseded as principal by Professor Keith Gull on 1 October 2009.
With David J. Wales he is the co-author of the textbook Introduction to Cluster Chemistry.