In this paper, the ultrafast dynamics of spin relaxation and recombination of photoexcited carriers has been studied in (001) GaAs quantum wells using a time-resolved pump-probe absorption spectroscopy under a nearly resonant excitation of heavy-hole excitons. It is found that the spin polarization of carriers influences both absorption saturation of linear polarized light and recombination dynamics of carriers. Pump fluence dependence of the ultrafast dynamics of spin relaxation and recombination of carriers is further studied, which shows that the effect of spin polarization on linearly polarized absorption saturation is reduced with lowering pump fluence. Spin-polarization-dependent absorption saturation effect can be ignored only as the pump fluence is weak. However, spin-polarization dependence of recombination dynamics is presented in turn at low pump fluence. Our analysis shows that such dependence originates from the spin-polarization dependence of the density of excitons formed in the excited carriers because recombination time constants of excitons and free carriers are very different so that the ratio of exciton density to free carrier density can influence the recombination dynamics. The spin-polarization dependence of ultrafast recombination dynamics of photoexcited carriers implies that the recombination time constant in the calculation of spin relaxation time from spin relaxation dynamics should be the recombination time of spin-polarized carriers, rather than the recombination lifetime of non-spin-polarized carriers as done currently. Exciton density is estimated based on 2D mass action law, which agrees very well with our experimental results. The good agreement between theoretical calculation and experimental results reveals that the effect of Coulomb screening on the formation of excitons may be ignored for a lower excited carrier density.