This manuscript introduces the principle and data processing method of a stepped mirror based temporally and spatially modulated imaging Fourier transform spectrometer. The instrument substitutes the moving mirror, which is widely used in a Michelson interferometer, with a stepped mirror to realize static interference. A scanning mirror is placed in front of the first imaging system to make the target image on different sub-mirrors to get different optical path differences. Light emitted from the target propagate through the scanning mirror and the first imaging system to focus on the stepped mirror and the plane mirror to form two primary images. The primary images are then reflected by the stepped and plane mirrors to propagate through the second imaging system and finally image on the detector. Since there are optical path differences between the stepped mirror and the plane mirror, the image captured by the detector would have the two-dimensional spatial and one-dimensional spectral information of the target. The scanning interval of the scanning mirror is set to be 0.095° according to the parameters of the stepped mirror and the optical system. Image stitching and spectrum reconstruction are done using the experimental data cube. A polar Hough transform based image cutting method is proposed to deal with the sub-mirror width difference problem in image cutting. To mitigate the discontinuity line effect in the panorama, the image is transformed to the HSI space to adjust its intensity. After interferogram dimension reduction, direct current offset removal, interferogram addressing, apodization, phase correction, Fourier transform and spectral resolution enhancement, the spectrum is reconstructed and its resolution is 194 cm-1, which is better than the designed value (250 cm-1).