We have carried out a theoretical study of the dynamics of the removal of one smectic layer from the N-layer free-standing smectic film during the layer-thinning process. Squeezing-out is initiated by a thermally activated nucleation process in which a density fluctuation forms a small hole. The dynamics of the bounding area during the layer-thinning transition N → N - 1, when the nucleation occurs in the center of the circular smectic film and the squeezed-out area increases up to the edge of the circular smectic area, is studied by the use of the conservation laws for mass and linear momentum. The disjoining pressure is the main factor that is responsible for the driving out of one smectic layer from the N-layer smectic film.