Micro/nano-electromechanical resonator-based logic elements have revitalized the notion of mechanical computing as a potential alternative to surpass the limitations of semiconductor electronics. A vital step forward for this technology is to develop a platform for cascadable logic units that communicate among each other executable signals of the same form; which is key to construct true and complex computation machines. Here, we utilize the dynamic characteristics of a clamped-clamped microbeam vibrating at the second resonance mode to realize cascadable logic elements. The logic operations are performed by on-demand activation and deactivation of the second mode of vibration of a clamped-clamped microbeam resonator. Fundamental logic gates, such as OR, XOR, and NOT, which constitute a functionally complete set for digital applications are demonstrated experimentally. We show that the demonstrated approach unifies the input and output signal waveform and performs all the gate operations on a single operating frequency, hence satisfying the prerequisites to realize cascadable resonator logic devices. This can potentially pave the way for the development of a novel technology platform for an alternative computing paradigm.