A Monte Carlo simulation study is performed to examine the effects of near-surface nonstoichiometry in a mixed-valent manganite (e.g., La0.7A0.3MnO3, where A=Sr, Ca) on the magnetization of its surface, and that of a few layers underneath. The nonstoichiometry is introduced either in the form of oxygen vacancy gradient or a gradient in the La:A ratio. The corresponding gradient in the exchange constant J is incorporated phenomenologically from the known phase diagram [P. Schiffer et al., Phys. Rev. Lett. 75, 3356 (1995)]. We show that the near-surface nonstoichiometry can account for the temperature dependence of magnetization of the surface layers as revealed by photoemission and x-ray magnetic circular dichroism (X-MCD) experiments [J. Park et al., Nature (London) 392, 794 (1998); J. Park et al., Phys. Rev. Lett. 81, 1953 (1998)]. The demagnetization shows viscous fingeringlike protrusions which may have important consequences for spin-polarized transport across interfaces.