One of the most important grinding parameters is the real depth of cut which is always lower than its programmed value. This is because in reality abrasive grains of the grinding wheel are not fixed but attached to a bonding material which is deformed during the process. In this study we investigate the effect of the contact stiffness between a single abrasive grain and the workpiece on the depth of cut and the grinding process characteristics via three-dimensional Molecular Dynamics (MD) simulations. Contact stiffness has been modelled by attaching a single trapezoid abrasive grain to a spring in the normal grinding direction. MD experiments have been repeated due to the stochastic nature of the grinding process in favour of statistical accuracy. Various grinding speeds have been considered while the case of a rough abrasive-workpiece interface has been investigated as well using fractal models. Our results indicate that the trajectory followed by the abrasive grain is not a straight line, as in the case of a rigid abrasive, but a curved one, asymptotically converging towards the equilibrium point which corresponds to the selected value of the spring stiffness. This behaviour alongside the grinding velocity and rough abrasive-workpiece interface have been found to affect the grinding forces, friction coefficient, morphology of the ground surface and subsurface temperature. The present MD model has also been proven to be capable of capturing the thermal softening phenomenon at the abrasive-workpiece interface.