The utility model relates to a garbage incinerator and a slag extractor. The garbage incinerator comprises a slag inlet well and a slag extractor water tank connected with the slag inlet well, wherein a slag pushing arm for transporting back and forth is further arranged below the slag inlet well; an automatic water supplementing device is arranged in the slag extractor water tank; the automatic water supplementing device comprises a water tank and an automatic water supplementing valve on the water tank; a hydraulic mud removing device is further arranged on the rear surface of the slag pushing arm. The garbage incinerator has the advantages that the wastewater can be introduced into the slag inlet machine for being recycled, the waste of water resources is reduced, the mud accumulation amount behind the pushing plate can be effectively controlled through the hydraulic automatic mud removing device, and the step of manually removing mud slag is avoided.