Spin pumping consists in the injection of spin currents into a nonmagnetic material due to the precession of an adjacent ferromagnet. In addition to the pumping of spin the precession always leads to pumping of heat, but in the presence of spin-orbital entanglement it also leads to a charge current. We investigate the pumping of charge, spin, and heat in a device where a superconductor and a quantum spin Hall insulator are in proximity contact with a ferromagnetic insulator. We show that the device supports two robust operation regimes arising from topological effects. In one regime, the pumped charge, spin, and heat are quantized and related to each other due to a topological winding number of the reflection coefficient in the scattering matrix formalism, translating to a Chern number in the case of Hamiltonian formalism. In the second regime, a Majorana zero mode switches off the pumping of currents owing to the topologically protected perfect Andreev reflection. We show that the interplay of these two topological effects can be utilized so that the device operates as a robust charge, spin, and heat transistor.