Future space X-ray telescopes, for example, the Lynx X-ray Observatory under study in the 2020 Astrophysics Decadal Survey, require high angular resolution, large field of view and large effective area X-ray mirrors. Various scientific, engineering and economic considerations make the manufacturing of the telescope optics challenging. In spite of many major improvements in current methods, including slumping (glass shaping), silicon pore optics, and monocrystalline silicon polishing, etc., the required resolution and stability in thin optics have not yet been demonstrated. Furthermore, the high reflective coating films on the mirrors can stress and distort the mirror figure. Therefore, additional steps to correct the mirrors are needed to achieve the stringent requirements for the next generation high-performance X-ray mirrors. In this paper, we demonstrate a novel X-ray mirror figure correction method with the use of femtosecond lasers. Over the last two decades, rapid developments of ultrafast laser technologies have triggered wide applications in the processing of both transparent and opaque materials, from material micromachining to nano-surgeries. We apply this technology in a novel stress-based figure correction technique for X-ray telescope mirrors. We use femtosecond laser beams to micromachine thermal oxide layers on the back side of silicon mirrors, from which regions of intrinsic compressive stress are removed. We pattern laser micromachined spots over the full mirror to compensate the undesired stress introduced from mirror manufacturing processes and reflective coatings. We built a new optics setup using an infrared laser of 220 fs pulse duration and 1 kHz repetition rate, and we designed a procedure for imaging, correcting and measuring mirror substrates with this setup. In this paper, we present the experimental results on the stress manipulation in at silicon substrates, showing the laser induced integrated stress increases almost linearly with the fraction of area removal in the micromachining. This indicates great potential for correcting thin silicon optics by using appropriate machining parameters for future X-ray telescopes.