A method for disposing of a mixture of oxidizable catalyst material and inert support media. The method comprises introducing inert gas into an enclosure. The enclosure contains a plurality of stacked screens, the stacked screens have openings that decrease in size from a top of the stack to a bottom of the stack. The method also comprises introducing the mixture to an uppermost one of the plurality of stacked screens; moving the plurality of stacked screens to cause the oxidizable catalyst material to separate from and migrate to a location beneath the inert support media; conveying the separated inert support media to a location outside the enclosure for disposal as non-hazardous waste; and conveying the separated oxidizable catalyst material to a location outside the enclosure for at least one of reclamation, or thermal destruction.