Photopolymerization-based additive manufacturing methods are promising approaches for fabricating intricate structures, especially on small scales, but generally limited to the use of a single material. Grayscale masked stereolithography (gMSLA) overcomes this limitation and facilitates the fabrication of structures with functionally graded material behavior. Generally, the mechanical properties and physical dimensions of the resulting parts depend on the crosslink density or degree of cure of the solidified photopolymer, which is related to the incident light energy during UV curing. In this research, we systematically investigate the influence of the main user-controllable process parameters in gMSLA, i.e., grayscale, exposure time, and layer thickness, on the resulting mechanical and geometrical properties. Based on the experimental studies, we unify these process parameters into a single controllable design parameter, the exposure intensity. We then develop elasto-visco-plastic constitutive models and geometric correction terms that describe the mechanical behavior and geometric deviations in terms of the exposure intensity. Here, plastic, viscoelastic, and elastic parameters are formulated as a function of exposure intensity. In this way, engineering design of parts with controllable and graded mechanical behaviors and reliable geometric dimensions with gMSLA is facilitated through an optimized choice of process parameters. In particular, we show that by choosing an appropriate parameter set, the print time can be significantly reduced while maintaining identical mechanical behavior. Furthermore, we show that the elasto-visco-plastic constitutive model accurately approximates the material behavior in uniaxial tension tests to failure, relaxation tests, and cyclic loadings. Overall, we observe an excellent agreement of the experimental results with numerical models for elasto-visco-plasticity during the entire process of constructing this framework for characterizing the influence of process parameters on gMSLA. This suggests that the results should be transferable to similar material systems and 3D printing technologies.