Apparatus and method for disassembling a toroidally shaped core is provided. The core is configured to carry a cured tire and includes multiple core segments extending generally radially from a central axis. The apparatus includes a base; one or more segment positioning devices connected for movement relative to the base and operative to move one or more core segments from an assembled core position next to an adjacent core segment around the central axis to a radially inward position; and one or more segment removal devices operatively connected for engaging the one core segment at the radially inward position and removing the one segment from the radially inward position to a remote position external to the core. The segment removal device operatively moves in three axes of motion to relocate the one segment from the remote position to a storage position and deposit the core segment at the storage station in a retrieval-ready orientation. All of the core segments may be moved sequentially in like manner by the segment removal device in order to disassemble the core.