Terahertz (THz) meta-devices are considered to be a promising framework for constructing integrated photonic circuitry, which is significant for processing the upsurge of data brought about by next-generation telecommunications. However, present active metasurfaces are typically restricted by a single external driving field, a single modulated frequency, fixed switching speed, and deficiency in logical operation functions which prevents devices from further practical applications. Here, to overcome these limitations, we propose a hybrid THz metasurface consisting of vanadium dioxide (VO2) and germanium (Ge) that enables electrical and optical tuning methods individually or simultaneously and theoretically investigate its performance. Each of the two materials is arranged in the meta-atom to dominate the resonance strength of toroidal or magnetic dipoles. Controlled by either or both of the external excitations, the device can switch on or off at four different frequencies, possessing two temporal degrees of freedom in terms of manipulation when considering the nonvolatility of VO2 and ultrafast photogenerated carriers of Ge. Furthermore, the “AND” and “OR” logic operations are respectively achieved at two adjacent frequency bands by weighing normalized transmission amplitude. This work may provide an auspicious paradigm of THz components, such as dynamic filters, multiband switches, and logical modulators, potentially promoting the design and implementation of multifunctional electro-optical devices in future THz computing and communication.