Surface plasmon polaritons in graphene can enhance the performance of mid-infrared spectroscopy, which is key for the study of both the composition and the conformation of organic molecules via their vibrational resonances. In this paper, a plasmonic biosensor using a graphene-based van der Waals heterostructure on a piezoelectric substrate is theoretically demonstrated, where far-field light is coupled to surface plasmon-phonon polaritons (SPPPs) through a surface acoustic wave (SAW). The SAW creates an electrically-controlled virtual diffraction grating, suppressing the need for patterning the 2D materials, that limits the polariton lifetime, and enabling differential measurement schemes, which increase the signal-to-noise ratio and allow a quick commutation between reference and sample signals. A transfer matrix method has been used for simulating the SPPPs propagating in the system, which are electrically tuned to interact with the vibrational resonances of the analytes. Furthermore, the analysis of the sensor response with a coupled oscillators model has proven its capability of fingerprinting ultrathin biolayers, even when the interaction is too weak to induce a Fano interference pattern, with a sensitivity down to the monolayer limit, as tested with a protein bilayer or a peptide monolayer. The proposed device paves the way for the development of advanced SAW-assisted lab-on-chip systems combining the existing SAW-mediated physical sensing and microfluidic functionalities with the chemical fingerprinting capability of this novel SAW-driven plasmonic approach.