This paper reports a study towards enhancing the throughput of the Atomic Force Microscope (AFM) tip-based nanomachining process by increasing the cutting speed at the interface between the tool and the workpiece. A modified AFM set-up was implemented, which combined the fast reciprocating motions of a piezoelectric actuator, on which the workpiece was mounted, and the linear displacement of the AFM stage, which defined the length of produced grooves. The influence of the feed, the feed direction and the cutting speed on the machined depth and on the chip formation was studied in detail when machining poly(methyl methacrylate). A theoretical cutting speed over 5 m/min could be achieved with this set-up when the frequency of the piezoelectric actuator reciprocating motions was 40 kHz. This is significantly better than the state of the art for AFM-based nanomachining, which is currently less than 1 m/min.