The Mn doping effects on the gate-tunable transport properties of topological Dirac semimetal Cd₃As₂ films have been investigated. Mn-doped Cd₃As₂ films are directly grown on GaAs(111)B substrates by molecular-beam epitaxy, during which the single crystal phase can be obtained with Mn concentration less than 2%. Shubnikov-de Haas oscillation and quantum Hall effect are observed at low temperatures, and electrons are found to be the dominant carrier in the whole temperature range. Higher Mn content results in smaller lattice constant, lower electron mobility and larger effective band gap, while the carrier density seems to be unaffected by Mn-doping. Gating experiments show that Shubnikov-de Haas oscillation and quantum Hall effect are slightly modulated by electric field, which can be explained by the variation of electron density. Our results provide useful information for understanding the magnetic element doping effects on the transport properties of Cd₃As₂ films.