Antiferromagnetic material possesses excellent robustness to an external magnetic field perturbation, which makes it promising in application of spintronic devices. The magnon-phonon interaction plays a vital role in spintronic devices. In this work, we performed first-principles calculation to study the effect of magnon-phonon interaction on magnon spectra of the antiferromagnetic MXenes Cr2TiC2FCl, and calculated the phonon dominated magnon relaxation time based on the magnon spectra broadening. Due to the large exchange constants across Cr-Cr pairs, high magnon energy is found in Cr2TiC2FCl. We find that compared with the acoustic magnons, the optical magnons have stronger interaction with phonon modes. Moreover, relaxation time of optical magnons and acoustic magnons have quite different wavevector dependence. Our results about spin coupling to specific phonon polarizations can shed light on the understanding of magnon damping and energy dissipation in two-dimensional antiferromagnetic materials.