To extend the life of a tool by preventing the chipping of the tool without deteriorating the bite-ability of the trimmed edge in the beginning of cutting-off in the cutting-off method when the edge pieces cut off by continuously trimming the edge portion of the steel strip by a side reamer is cut off into a strip shape by a scrap chopper composed of a pair of scrap chopper rotors.

The lower limit value of the rotation of the rotor is maintained for a period of 0.5 to 3 sec from the start of the cutting-off such that the peripheral speed of the rotor becomes 30 to 50 m/min. After that, the rotational speed of the rotor is controlled so as to be V=av, where V is the peripheral speed of the rotor, v is the inlet speed of the trimmed edge, and a1.