Recently, van der Waals (vdW) two-dimensional heterostructures have attracted great attention. The combination structures demonstrate unique properties that individual layers do not possess, which foretell promising future applications. Here, we investigate the structural and electronic properties of SiC/graphene, SiC/MoS2, and graphene/SiC/MoS2 vdW heterostructures using first-principles calculations. The SiC/graphene interface forms a p-type Schottky contact, which can be turned into an n-type Schottky contact by applying an external electric field. Moreover, a transition from a Schottky to an Ohmic contact at the interface can be triggered by varying the interlayer distance or applying an external electric field. The SiC/MoS2 interface forms a type-II heterostructure, in which the recombination of photoexcited charges will be greatly suppressed. The transition from type-II to type-III band alignment can be realized in the SiC/MoS2 heterostructure by applying a biaxial strain. This heterostructure also shows excellent optical absorption abilities in the visible and far-infrared range, which merits its application as a photocatalyst. The trilayer heterostructure exhibits a tunable Schottky barrier with different stacking patterns and the assembled graphene could act as a protective encapsulating layer on SiC/MoS2. The results show that graphene and MoS2 can tune and improve the electronic performance of SiC and demonstrate the promising application of SiC-based heterostructures for nanoelectronics and nanophotonics.