This paper presents a novel penalized multi-response Taguchi method that is used to determine the optimal conditions and parameters for a wheel-type magnetorheological (MR) finishing process that uses sintered iron-carbon nanotube (I-CNT) abrasives. The main goal of this study is to achieve the best compromise, within given boundary constraint conditions, between the maximum material removal rate and the minimum surface roughness. The proposed Taguchi method includes two main parameters, namely the weighting loss factor and the severity factor, that account, respectively, for the response weights and the constraint conditions and that control the optimality direction. The method is applied to the finishing of hard-disk slider surfaces made of Al2O3-TiC, and the effects of the weighting loss and severity factors, along with their significance and relative importance in optimizing the finishing process, are thoroughly examined.