The presence of species other than the target biomolecules in the fluidic analyte used in the refractive index biosensor based on the surface plasmon resonances (SPRs) can lead to measurement ambiguity. Using graphene-based acousto-plasmonic biosensors, we propose two methods to eliminate any possible ambiguity in interpreting the measured results. First, we take advantage of the dynamic tunability of graphene SPRs in the acousto-plasmonic biosensor with a surface acoustic wave (SAW) induced uniform grating, performing measurements at different applied voltages. Second, a single measurement employing a similar biosensor but with SAW-induced dual-segment gratings. The numerical results show the capability of both methods in decoupling the effect of the target analyte from the other species in the fluid, enabling interpreting the measurement results with no ambiguity. We also report the results of our numerical investigation on the effect of measuring parameters like the target layer effective refractive index and thickness, and the fluid effective refractive index, in addition to the controlling parameters of the proposed acousto-plasmonic biosensor, including graphene Fermi energy and electrical signaling on the sensing characteristics. Both types of proposed biosensors show promising features for developing the next generation lab-on-a-chip biosensors with minimal cross-sensitivities to non-target biomolecules.