This study quantifies how geotechnical parameter uncertainty propagates to the post-failure kinematics of retrogressive landslides in sensitive clays under large deformation. Instead of relying on a global Factor of Safety, which cannot represent progressive strength loss and post-peak motion, two physically meaningful response measures are adopted: (i) retrogression distance (crest retreat) and (ii) run-out distance (downslope reach). A saturated undrained formulation is considered, and the soil response is described by a continuous strain-softening Mohr–Coulomb model that degrades strength from peak to residual as accumulated plastic strain increases; large-deformation solution strategies such as the Material Point Method (MPM) provide a convenient framework to simulate the associated kinematics. Uncertainty is introduced in four key variables—peak cohesion, residual cohesion, a softening shape factor, and soil density—using mean values and coefficients of variation from the literature on sensitive clays. Two moment-based probabilistic schemes are employed: the First-Order Second-Moment method (FOSM) with two-sided finite differences, and Rosenblueth’s Point Estimate Method (PEM). A total of 25 large-deformation simulations are performed (9 for FOSM and 16 for PEM). Results show that the framework captures progressive failure and large displacements, while FOSM/PEM provide efficient estimates of the mean and dispersion of retrogression and run-out at a computational cost far below full Monte Carlo. Residual cohesion consistently dominates the variability of both responses, whereas the softening factor mainly affects the upper tail of retrogression. The proposed approach supports consequence-oriented, probabilistic hazard assessment of sensitive-clay slopes based on exceedance probabilities of critical retrogression/run-out thresholds.