As a promising device of vibration isolation for rocket engine turbopumps, turbine engines, and other kinds of rotordynamic applications, the elastic porous metal mesh damper (MMD) has drawn large attention from researchers. It exhibits higher load capacity and environmental adaptivity than traditional viscoelastic damping materials owing to the excellent combination of metallic properties and the rubber-like damping performance. However, the design of a metal mesh damper relies heavily on the trial-and-error methodology for tuning fabrication parameters, which prevents it from widespread use in rotor-bearing applications. Therefore, efforts are directed toward forging an explicit link between fabrication parameters and the dynamic behaviors of MMDs in the present work. Quasistatic and dynamic mechanical tests are carried out to help determine the primary factor that influences the damping performance of the MMD and to demonstrate how the dynamic behaviors of MMDs evolve with the fabrication parameters. Furthermore, two different modeling methodologies, i.e., the FE method and the mixed damping approach, are used to predict the hysteresis behaviors of the dampers. The latter method not only properly reproduces the experimental results but also makes it possible to build an intuitive connection between the fabrication procedures and the dynamic mechanical behaviors of the MMDs. The orthogonal test results determine that the mesh density plays a dominant role in controlling both the load capacity and damping performance of the MMDs. By integrating mesh density and motion amplitude into the expression of parameters including stiffness coefficient, damping coefficient, and damping component factor, the mixed damping model demonstrates excellent predictive accuracy under different excitation conditions.