Embodiments of a methods for producing gas turbine engine rotors and other powdered metal articles having shaped internal cavities are provided. In one embodiment, the method includes consolidating a powdered metal body utilizing a hot isostatic pressing process to produce a rotor preform in which elongated sacrificial tubes are embedded. Acid or another solvent is directed into solvent inlet channels provided in the elongated sacrificial tubes to chemically dissolving the elongated sacrificial tubes and create shaped cavities within the rotor preform. The rotor preform is subject to further processing, such as machining, prior to or after chemical dissolution of the elongated sacrificial tubes to produce the completed gas turbine engine rotor.