Azurin (Az) has been considered as the research hotspot in molecular electronics, as well as a promising material for building functional devices on the molecular scale because of its special electrical properties and force-dependent conductance effects. Here we carry out an in-depth investigation combined with molecular scale experiments, molecular dynamics simulations, first-principles calculations and theoretical models to reveal the dynamic conductance response of the Az monolayer under cyclic mechanical loading. Experimentally, the conductance of the Az monolayer under continuous cyclic loads was recorded using a conductive atomic force microscope. Our results demonstrate the strong nonlinear force-dependence and significant time-delayed characteristics, which distinctly differ from the results obtained under stepwise loading. It is also found that the period and amplitude of cyclic loads have a great impact on the magnitude, peak value and change rate of the current. The regular dynamic response of the Az conductance under mechanical force looks like a type of memristive behavior, which is defined as mechanics-modulated memristive behavior in this work. In order to verify these peculiar experimental results, we employed both molecular dynamics simulations and first-principles calculations to analyze the structural deformation and molecular orbitals of Az under cyclic loads. A phenomenological model is also established to explain experimental findings and further illustrate mechanics-modulated memristive behavior.