A blade cover covers a cutting blade mounted on a spindle. The blade cover has a bottom portion formed with an opening from which the lower end of the cutting blade projects. A cutting fluid is supplied to the upper surface of a workpiece in the periphery of the opening of the blade cover. A discharge opening is formed in the blade cover. Air is sucked from the discharge opening by a vacuum source. The cutting fluid supplied to the upper surface of the workpiece is taken from the opening into the blade cover in association with the rotation of the cutting blade and thereafter discharged from the discharge opening to the outside of the blade cover. Accordingly, scattering of the cutting fluid can be suppressed.