Approaches to generate and manipulate Cherenkov radiation (CR) are challenging yet meaningful. Optical topological transition (OTT) in novel materials and metamaterials is also promising for modern photonics. We study the OTT of CR in graphene-based hyperbolic metamaterials (GHMs) for the first time. In GHMs, conventional and hyperbolic CR can be switched when crossing the topological transition frequency. This frequency can be altered by metamaterial components and external optical elements. For instance, external ultrafast optical pumps cause an ultrafast OTT from the elliptical to the hyperbolic state. Then, hyperbolic CR can be excited by low-energy electrons by leveraging the excellent photothermal properties of graphene. Hyperbolic CR vanishes when the GHM returns to its original state. Furthermore, graphene nonlocality occurs when the electron velocity is low enough, corresponding to a large wave vector. Concretely, when the electron velocity approaches the Fermi velocity of graphene, a nonlocality-induced OTT modifies the plasmonic properties of the GHM and brings a new lower velocity threshold of hyperbolic CR. Therefore, hyperbolic CR can only be induced in a limited velocity range. These findings pave the way for understanding CR properties in active plasmonic metamaterials and may be applied to complex photonic and polaritonic systems.