Micrometric-thin cells (MCs) with alkali vapor atoms have been valuable for research and applications of hyperfine Zeeman splitting and atomic magnetometers under strong magnetic fields. In this paper, the saturated absorption spectra using a 100-μm cesium MC are studied theoretically and experimentally, where the pump and probe beams are linearly polarized beams with mutually perpendicular polarizations, and the magnetic field is along the pump beam. Because of the distinctive thin chamber of the MC, crossover spectral lines in saturated absorption spectra are largely suppressed leading to clear splittings of hyperfine Zeeman transitions in experiments, and the effect of spatial magnetic field gradient is expected to be reduced. A calculation method is proposed to achieve good agreements between theoretical calculations and experimental results. This method successfully explains the suppression of crossover lines in MCs, as well as the effects of magnetic field direction, propagation and polarization directions of the pump/probe beam on saturated absorption spectrum. The saturated absorption spectrum with suppressed crossover lines is used for laser frequency stabilization, which may provide the potential value of MCs for high spatial resolution strong-field magnetometry with high sensitivity.