Based on the phase-transition property of vanadium dioxide (VO2), a terahertz bifunctional absorber is proposed with switchable functionalities of broadband absorption and multiband absorption. When VO2 is metal, the system is regarded as a broadband absorber, which is composed of VO2 patch, topas spacer, and VO2 film with metallic disks inserted. The system obtains a broadband absorption with absorptance >90% from 3.25 THz to 7.08 THz. Moreover, the designed broadband absorber has a stable performance within the incident angle range of 50°. When VO2 is dielectric, multiband absorption with six peaks is realized in the designed system. Graphene and the metallic disk-shaped array play the dominant role in the mechanism of multiband absorption. Through changing the Fermi energy level of graphene, the performance of multiband absorption can be dynamically adjusted. Because of the switchable functionalities, the proposed design may have potential application in the fields of intelligent absorption and terahertz switch.