Three-dimensional Molecular Dynamics simulations have been performed to investigate the effects of fractal roughness on nanoscale grinding. The first part of this investigation focuses on the effects of the workpiece rough top surface on the grinding process characteristics, with special emphasis placed on the friction coefficient, the grinding forces and the subsurface temperature. The second part focuses on the alternation of the aforementioned parameters due to the rough abrasive contact surface. Rough surface profiles have been generated using the multivariate Weierstrass-Mandelbrot function while the abrasive has been modelled as a trapezoid. The irregular surface topography has been controlled by tuning the value of the fractal dimension Ds . The aforementioned experiments have been repeated for various values of the cutting depth. Our results indicate that the grinding process parameters are mainly dependent on the cutting depth as well as the abrasive lower surface profile, which also defines the interface contact area between the workpiece and the abrasive, rather than the topography of the workpiece top surface.