In order to predict the correlation among the processing parameters, microstructures, and mechanical properties for additive manufacturing, a computational framework integrating discrete element method, phase-field simulation, crystal plasticity finite element method, and extreme value statistics is proposed. The framework is applied to reveal the influence of laser scanning velocity on the microstructure evolution, yield stress, and fatigue dispersity. Firstly, discrete element method is applied to spread the powder bed layer by layer. The spreading is performed on the curved surface of the previously solidified layer. Secondly, the heat-melt-microstructure coupled non-isothermal phase-field simulations are performed to obtain the temporal and spatial evolution of melt, pore, grain boundary, grain distribution/orientation, etc., as well as the final polycrystal microstructure. Thirdly, crystal plasticity finite element method is utilized to attain the macroscopic mechanical response of the additively manufactured polycrystal microstructure (AMPM) and the fatigue indicator parameter (FIP) which is a surrogate measure for the driving force to form fatigue cracks. Fourthly, extreme value statistics are carried out to analyze the extreme value distribution of FIPs and the fatigue dispersity of the AMPM. Simulation results on the selective laser melting based additive manufacturing of 316L stainless steel powder indicate that the macroscopic yield stress of the AMPM is anisotropic and decreases with the increasing laser scanning velocity. The extreme value of FIPs from the AMPM with random distribution of grain orientations correlates well with the Gumbel extreme value distribution. The increase of laser scanning velocity could decrease the fatigue dispersity of the AMPM, but increase the FIP extremum and the associated driving force for fatigue crack initiation and thus further decrease the fatigue life.