Interferometers and resonant cavities are indispensable driving mechanisms for compact, high-speed, and low-power modulators and switches in modern signal processing systems. However, their limitations in key performance metrics critically restrict present data-processing capabilities. Here, a completely different wave-modulation mechanism is proposed based on non-Hermitian dynamics near an exceptional point (EP) singularity. The proposed modulator is enabled by EP-bypassing adiabatic processes that exclusively select different final states depending on active trigger signal possibly at indefinitely small magnitude in principle. Importantly, this operation principle does not involve any explicit frequency-dispersive feature in stark contrast to interference or resonance effects. In addition, it can be implemented in available device-engineering platforms such as integrated optical circuits. Therefore, it is of great interest to further investigate the proposed principle for improved signal-processing systems on forthcoming demand.