PURPOSE: To prevent damage to a cutting tool provided on a traveling cutoff machine, by stopping the cutoff of a metal material when the difference between the conveyance speed of the metal material and the moving speed of the traveling cutoff machine is larger than an allowable value.

CONSTITUTION: In a method of cutting off a continuously conveyed metal material to a prescribed dimension by using a traveling cutoff machine, the absolute value Vm-Vc of the difference between the conveyance speed Vm of a steel pipe 1 as the metal material and the moving speed Vc of a casing 21 is detected so that the steel pipe is not cutoff when the detected absolute value is larger than an allowable level a set on a comparator 31. A thrusting force which would damage a cutting tool 28 is thus prevented from being caused. As a result, the cutting tool 28 provided on the traveling cutoff machine 2 is not damaged. Althrough the cutoff machine 2 is provided with a clamp 27, this invention can be also applied to a traveling cutoff machine not provided with such a clamp.