Capture of a prey by spider orb webs is a dynamic process with energy dissipation. The dynamic response of spider orb webs under prey impact requires a multi-scale modeling by considering the material microstructures and the assembly of spider silks in the macro-scale. To better understand the prey capture process, this paper addresses a multi-scale approach to uncover the underlying energy dissipation mechanisms. Simulation results show that the microstructures of spider dragline silk play a significant role on energy absorption during prey capture. The alteration of the microstructures, material internal friction, and plastic deformation lead to energy dissipation, which is called material damping. In addition to the material damping in the micro-scale modeling, the energy dissipation due to drag force on the prey is also taken into consideration in the macro-scale modeling. The results indicate that aerodynamic drag, i.e., aero-damping, plays a significant role when the prey size is larger than a critical size.