The mechanism of anodic dissolution of microroughnesses in the combined method of anodic-abrasive vibratory polishing with magnetic-abrasive electrically polarized charged grains of channels of pipes of small cross section made of non-magnetic materials is presented. Materials that can be used as magnetic-abrasive composite grains such as Fe3C, FeB, FeB2, etc. or magnetic NbC-Fe modified with graphene, carbon nanotubes, or a combination thereof have been selected. A passivating electrolyte used in this combined method of vibration anode-abrasive polishing, for example, 3% NaNO3 + (3-6)% Fe3C, is proposed. The article shows the developed scheme of the process of combined magnetic-abrasive polishing and describes the process itself. The value of the allowance to be removed can be estimated from the proposed formula for calculating the removed layer of microroughness in the joint electrochemical process of polishing the channel surface with stationary and pulsed currents flowing in the electrolyte flow.