A mist/dust collector includes a tank body, a recovery tank having a demister member, a spraying unit spraying water or coolant fluid from a nozzle, an impeller mounted on a main shaft located in the tank body, so as to be rotatable by air flow, a disc rotary brush and a shaking-off member mounted on the shaft. A suction unit is actuated to draw air containing mist and dust into the tank body interior maintained in a negative pressure state. The impeller is rotated by collision of water or coolant fluid at a predetermined pressure, and the rotary brush and the shaking-off member are rotated simultaneously with the impeller, so that mist and dust are separated from air by a centrifugal action of the rotary brush and the shaking-off member. Mist and dust remaining in the air flowing into the recovery tank are collected by the demister member.