To provide a cutting machine equipped with an easy torch hood with long life by using of plasma arc or laser capable of efficiently shielding sputters and easily watching cutting conditions and changing torch supplies, and a cutting method.

In a cutting machine for cutting metals by plasma arc (22) or laser emitted from a torch (4), a hood (11), which can be raised and lowered by an actuator (15), is installed around the torch (4). A controller (10) controls to lower, at least at the time of piercing, the hood (11) to a position for covering the torch (4) by commanding to the above actuator (15). And during piercing, cutting, or changing torch supplies, a method for selectively raising and lowering the hood (11) at the fixed height as needed is good.