In this paper, the ordered single-open-chain (SOC) method in combination with the principle of virtual work is adopted to model and solve the forward dynamics of a single degree-of-freedom (DOF) parallel mechanism (PM), featuring one translation and two rotations (1T2R), which is applied in spatial vibrating screen (i.e., parallel vibrating screen mechanism, PVSM). Afterwards, the dynamic performances of the PVSM is optimized using differential evolution algorithm. Based on the kinematics of the PM, the forward dynamic model is derived and the dynamic response equation is built, of which the coefficient matrix is determined by means of the generalized velocity equation. Moreover, the Euler method was adopted to solve the numerical solution of the differential equation of motion to characterize the motion law and dynamics of the screen surface of the PVSM, which is verified with ADAMS simulation. With the parametric model, the dynamic optimization of PVSM is carried out to maximize the energy transfer efficiency, subject to the constraints on the link mass. The comparison of the dynamic performances of the PVSM with and without optimization reveals the improvement of the PM.