There are provided a tape printing apparatus and a tape printing method, which are capable of setting or determining whether or not half-cutting should be carried out, based on the detected type of a tape set for use, as well as a cutting device capable of detecting the type of a tape-shaped member, and setting whether or not the tape-shaped member should be cut, based on the detected type of the tape-shaped member, a tape printing apparatus incorporating the device, and a method for the cutting device. The tape printing apparatus has a half-cutting function of cutting only a peel layer of a tape-shaped member formed of an image-receiving layer and the peel layer and by using a half-cutting tape cutter in the direction of the width of the tape-shaped member. The type of the tape-shaped member is detected. Whether or not the half-cutting tape cutter is driven, based on a result of the detection. Printing is carried out on the tape-shaped member. When the half-cutter is set to be driven, the half-cutting tape cutter is driven to perform half-cutting of the image-receiving layer alone of the tape-shaped member at a forward location of the tape-shaped member in the direction of feed thereof.