Provided are a method and a device for efficiently separating and automatically removing a tire-building rigid core from the inside of the tire. After a core holding mechanism and upper and lower support plates are removed from a rigid core body that is disposed in the tire and composed of two types of segment groups, the tire is transferred onto a predetermined position on a support table, and positioned and fixed. Then, a first core separation/removal mechanism having been on standby below the center of the tire on the support table is raised to support the center of the inner wall surface of one type of the segment groups and horizontally pull the one type of the segment groups to the center side of the tire until it is separated from the inner surface of the tire. The separated segment group is lowered to the standby position below the center of the support table and is left on standby. Next, in the same way as above, the other type of the segment groups is separated from the inner surface of the tire and moved to a standby position by a second core separation/removal mechanism having been on standby at another standby position.