A grinding machine includes an abrasive element rotatably mounted on a support frame and coupled to a drive, a blower casing including a surrounding wall which confines a blower chamber and which extends beyond and which is spaced apart radially from a rim of the abrasive element to define a surrounding intake passage therebetween, a dust discharge port disposed downstream of the intake passage, communicated with the blower chamber and, and offset from an axis of the abrasive element, and an impeller disposed in the blower chamber and coaxial with the abrasive element such that dust generated as a result of a grinding operation of the abrasive element is entrained in an air stream drawn into the blower chamber through the surrounding intake passage and subsequently out of the discharge port by virtue of rotation of the impeller.