As a research upsurge, van der Waals (vdW) heterostructures give rise to numerous combined merits and novel applications in nanoelectronics fields. Here, we systematically investigate the electronic structure of MnPSe3/CrSiTe3 vdW heterostructures with various stacking patterns. Then, particular attention of this work is paid on the band structure modulations in MnPSe3/CrSiTe3 vdW heterostructures via biaxial strain or electric field. Under a tensile strain, the relative band edge positions of heterostructures transform from type-I (nested) to type-II (staggered). The relocation of conduction band minimum also brings about a transition from indirect to direct band gap. Under a compressive strain, the electronic properties change from semiconducting to metallic. The physical mechanism of strain-dependent band structure may be ascribed to the shifts of the energy bands impelled by different superposition of atomic orbitals. Meanwhile, our calculations manifest that band gap values of MnPSe3/CrSiTe3 heterostructures are insensitive to the electric field. Even so, by applying a suitable intensity of negative electric field, the band alignment transition from type-I to type-II can also be realized. The efficient band structure modulations via external factors endow MnPSe3/CrSiTe3 heterostructures with great potential in novel applications, such as strain sensors, photocatalysis, spintronic and photoelectronic devices.