Understanding the deformation mechanisms in multilayer graphene (MLG), an attractive material used in nanodevices as well as in the reinforcement of nanocomposites, is critical yet challenging due to difficulties in experimental characterization and the spatio-temporal limitations of atomistic modeling. In this study, we combine nanomechanical experiments with coarse-grained molecular dynamics (CG-MD) simulations to elucidate the mechanisms of deformation and failure of MLG sheets. Elastic properties of graphene sheets with one to three layers are measured using film deflection tests. A nonlinear behavior in the force vs. deflection curves for MLGs is observed in both experiments and simulations - during loading/unloading cycles, MLGs dissipate energy through a "recoverable slippage" mechanism. The CG-MD simulations further reveal an atomic level interlayer slippage process and suggest that the dissipated energy scales with film perimeter. Moreover, our study demonstrates that the finite shear strength between individual layers could explain the experimentally measured size-dependent strength with thickness scaling in MLG sheets.