We report, using molecular dynamics simulation studies, how and under what conditions graphene layers separate, fold and shear during a wedge-based mechanical exfoliation machining technique to produce few-layer graphene. Our previously reported experimental results using this novel technique have shown clear evidence of few-layer graphene being subjected to such phenomena. Molecular simulations of initial wedge engagement show that the entry location of the wedge tip vis-á-vis the nearest graphene layer plays a key role in determining whether layers separate or fold and which layers and how many of them fold. We also show that depending on this entry location several successive layers beneath the wedge undergo significant elastic bending, consuming energies requiring large vertical forces to be imposed by the moving wedge. The layer separation force itself is seen to be minimal and consistent with breaking up of van der Waals interactions. In addition, shearing of layers occurs mainly during wedge exit and depends largely on the wedge speed and also its depth of insertion. Understanding the conditions at which this separation, folding and shearing of the graphene layers takes place, one can control or tune the wedge-based exfoliation technique for particular kinds of graphene layers.