Given the recent development of agile optical satellites for rapid-response land observation, side-oblique image-motion (SOIM) detection and blur correction have become increasingly essential for improving the radiometric quality of side-oblique images. The Chinese small-scale agile mapping satellite Kuaizhou-1 (KZ-1) was developed by the Harbin Institute of Technology and launched for multiple emergency applications. Like other agile satellites, KZ-1 suffers from SOIM blur, particularly in captured images with large side-oblique angles. SOIM detection and blur correction are critical for improving the image radiometric accuracy. This study proposes a SOIM restoration method based on segmental point spread function detection. The segment region width is determined by satellite parameters such as speed, height, integration time, and side-oblique angle. The corresponding algorithms and a matrix form are proposed for SOIM blur correction. Radiometric objective evaluation indices are used to assess the restoration quality. Beijing regional images from KZ-1 are used as experimental data. The radiometric quality is found to increase greatly after SOIM correction. Thus, the proposed method effectively corrects image motion for KZ-1 agile optical satellites.