Screening techniques have been widely deployed in industrial production for the size-separation of granular materials such as coal. The elliptical vibrating screen has been regarded as an excellent screening apparatus in terms of its high screening efficiency and large processing capacity. However, its fundamental mechanisms and operational principles remain poorly understood. In this paper, the sieving process of an elliptical vibrating screen was numerically simulated based on the discrete element method (DEM), and an approach coupling the DEM and the finite element method (DEM−FEM) was introduced to further explore the collision impact of materials on the screen deck. The screening time, screening efficiency, maximum stress and maximum deformation were examined for the evaluation of sieving performance. The effects of six parameters—length of the semi-major axis, length ratio between two semi-axes, vibration frequency, inclination angle, vibration direction angle and vibration direction—on different sieving results were systematically investigated in univariate and multivariate experiments. Additionally, the relationships among the four performance indexes were discussed and the relational functions were obtained. The conclusions and methodologies presented in this work could be of great significance for the design and improvement of elliptical vibrating screens.