We report the occurrence of vibrational resonance (VR) for a particle placed in a nonlinear asymmetrical Remoissenet-Peyrard potential substrate whose shape is subjected to deformation. We focus on the possible influence of deformation on the occurrence of vibrational resonance (VR) and show evidence of deformation-induced double resonances. By an approximate method involving direct separation of the time scales, we derive the equation of slow motion and obtain the response amplitude. We validate the theoretical results by numerical simulation. Besides revealing the existence of deformation-induced VR, our results show that the parameters of the deformed potential have a significant effect on the VR and can be employed to either suppress or modulate the resonance peaks, thereby controlling the resonances. By exploring the time series, the phase space structures, and the bifurcation of the attractors in the Poincaré section, we demonstrate that there are two distinct dynamical mechanisms that can give rise to deformation-induced resonances, viz., (i) monotonic increase in the size of a periodic orbit and (ii) bifurcation from a periodic to a quasiperiodic attractor.