PURPOSE: To perform the cutting with satisfactory accuracy without deteriorating the permeability of the energy flow with respect to a workpiece by providing a means to perform the cutting while releasing the support at the position where supporting columns to support the workpiece oppose to a cutting head.

CONSTITUTION: The titled cutting device 1 is provided with the cutting head 5 having a nozzle 3 to supply the energy flow and work table 7 to support the workpiece W is arranged under the cutting head 5. The work table 7 is moved relatively in the direction of X and Y axes with respect to the cutting head 5. The plural supporting columns 23 to support the workpiece W are arranged in proper intervals to each beam 21 of the work table 7. Only when said supporting columns 23 are situated at the position in opposition to the cutting head 5, the supporting columns 23 of the position are moved downward by an action of a lever, etc., and the cutting is performed in a state with the support of the workpiece W released.