The invention relates to a washing machine reduction clutch and a washing machine. The reduction clutch comprises an input shaft, a reduction gear, a clutch device, an output shaft, and an output shaft sleeve. The clutch device is at least partially arranged on the periphery of the circumferential direction of the reduction gear. The clutch device at least comprises a clutch shaft sleeve which can move in an axial direction. The clutch shaft sleeve is arranged out of an inner gear ring of the reduction gear, and is connected with the inner gear ring in a manner that the axial direction of the inner gear ring can slide relative to the clutch shaft sleeve and the circumferential direction of the inner gear ring cannot rotate relative to the clutch shaft sleeve. The clutch shaft sleeve axially moves to control different output states of the output shaft and the output shaft sleeve. The clutch device is arranged on the periphery of the circumferential direction of the reduction gear, and the axial space which is occupied by the clutch device originally is saved, so as to reduce integrated height of the reduction clutch, and reduce volume of the washing machine under the condition that washing capacity is not changed, or increase washing capacity under the condition that the volume of the washing machine is not changed.