Graphene has been proposed as an advanced plasmonic material spanning from infrared to terahertz (THz) bandwidth due to its advantages, such as electrical tunability, high carrier mobility, and low energy loss, etc. Therefore, plasmonic devices based on graphene have great potential in active tuning of the plasmon resonances through electrical doping. However, a major drawback of the electrically tuning is that the metal electrodes used in this scheme may increase the complexity of device fabrication and decrease the effective area for wave-graphene interaction. Optically tuning is an alternative to resolve this problem. Here we present a theoretical study on the THz responses and plasmonic properties of graphene-based heterostructures (GBHSs) in the presence of visible irradiation. More concretely, by combining classical electromagnetic theory with the dynamic graphene conductivity under optical pumping, we establish analytical models to describe the THz basic/plasmonic responses of GBHSs including graphene/substrate, cavity with graphene, and graphene/dielectric/dimple-array systems. Meanwhile, the effects of the power of the modulation/pumping light on the plasmonic resonances are also illustrated. The results obtained here are expected to help us to explore the potential applications in new type of graphene-based plasmonic devices, such as all-optical modulators, sensors, and filters.