We study the connection between the observed star formation rate-stellar mass (SFR-M-*) relation and the evolution of the stellar mass function (SMF) by means of a subhalo abundance matching technique coupled to merger trees extracted from an N-body simulation. Our approach, which considers both galaxy mergers and stellar stripping, is to force the model to match the observed SMF at redshift z > 2, and let it evolve down to the present time according to the observed SFR-M-* relation. In this study, we use two different sets of SMFs and two SFR-M-* relations: a simple power law and a relation with a mass-dependent slope. Our analysis shows that the evolution of the SMF is more consistent with an SFR-M-* relation with a mass-dependent slope, in agreement with predictions from other models of galaxy evolution and recent observations. In order to fully and realistically describe the evolution of the SMF, both mergers and stellar stripping must be considered, and we find that both have almost equal effects on the evolution of SMF at the massive end. Taking into account the systematic uncertainties in the observed data, the high-mass end of the SMF obtained by considering stellar stripping results in good agreement with recent observational data from the Sloan Digital Sky Survey. At log M-* < 11.2, our prediction at z = 0.1 is close to Li & White data, but the high-mass end (log M-* > 11.2) is in better agreement with D'Souza et al. data which account for more massive galaxies.