The High-Velocity Abrasive Cutting Tool has special port positioning for directing an abrasive fluid jet stream into the ID of the pipe to be severed. Running this abrasive cutting tool with the Titan downhole motor and a special mixture of abrasive fluids accomplishes a complete severing of the tubular. As the cutting head rotates below the motor, the abrasive fluids penetrate and sever the tube where the jet stream makes contact. The result is a clean-cut without any flaring of the tubular.