A device for separating and removing a rigid core when building a tire, including a slide table and positioning means which are provided on a support table of the separation/removal device. The slide table is slidable to convey the tire, whose inner surface is held by the rigid core body and a core holding mechanism, to a central position on the support table. An elevating device is provided on the central axis of the support table, and includes a clamping means to elevate the rigid core body and the tire from which the core holding mechanism is removed, to a position where the rigid core body and the tire do not interfere with the core holding mechanism. A pair of core separation/removal mechanisms are disposed below the center of the support table, capable of elevating movement, and radially contracting and removing each type of the segment groups.