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[en] Highlights: • Competitive effects from different mechanisms are presented for the title reaction. • The isotopic effects between H + MgH and D + MgD reactions are studied. • This work is a good example for other roaming related system. The dynamics of the D + MgD reaction at low collision energies are conducted in quasi-classical trajectory method (QCT) on three reaction channels, namely nonreactive, D abstraction, and D exchange. Isotopic effects between D + MgD and H + MgH reactions are included mainly in the exchange channel involving both direct and roaming mechanisms. The integral cross sections (ICSs), differential cross sections (DCSs) and state distributions at collision energies ranging from 1 to 9 kcal/mol are presented to show the dynamics and isotopic effects. Important difference can be found in the ro-vibrational state distributions between MgD2 and MgH2 systems.