To improve the productive efficiency without additional labor by feeding cutting oil to an appropriate position even when the width of a work is changed.

Supporting members 29A, 29B are provided on a fixing side vice jaw 7A capable of holding and releasing a work W provided on a cutting machine, e.g. a horizontal band sawing machine, and a moving side vice jaw 7B, a supporting plate 39 provided with a cutting oil nozzle 43 is movably provided on a shaft 31 fitted to the supporting members 29A, 29B, and coil springs 47A, 47B which are elastic members are provided between both sides of the supporting plate 39 and inner surfaces 35A, 35B of the supporting members 29A, 29B. Even when the width of the work W is changed, the position of the cutting oil nozzle 43 is changed to follow the width, and because the cutting oil nozzle 43 can be constantly positioned around the work W, the productive efficiency can be improved without additional labor.