To provide a foaming material cutting machine and a cutting method of a foaming material capable of cutting the foaming material at low cost without a trouble of a burn and an electric shock.

A rectilineal fine line 1 is held in a tensional state between upper and lower ratchet parts 17, 32 of a jigsaw machine 11 for foaming material cutting by tensing it by pulling it in the vertical direction. A thermoplastic synthetic resin material such as foaming styrene is cut mainly by frictional heat by reciprocating the fine line 1 in the axial direction at high speed by crank devices 27-29 with a motor 26 in the same jigsaw machine 11 as a driving source.