A vial-based system and method for handling and processing specimens of particulate matter-containing liquid directly in the vial. A processing assembly, which includes a stirrer and a particulate matter separation chamber, is releasably coupled to the inside of the vial cover. The processing assembly remains with the cover when the vial is opened to insert a specimen therein. Application of a particular external force to the closed vial detaches the processing assembly from the cover so that it remains in the vial, for access by automated or manual laboratory equipment, when the cover is subsequently removed.