A process for manufacturing an abrasive wire formed by abrasive particles held on a central core by a binder comprises depositing abrasive particles on the central core, each particle comprising a magnetic material that has a relative permeability greater than 50 and that represents at least 1% of the volume of the abrasive particle, and depositing binder on the central core to keep the abrasive particles attached to it. The core has south poles and north poles alternating along either its circumference or its length.