Pervious concrete is an eco-efficient concrete but has problems regarding its mechanical performance and permeability balance. This research investigated the feasibility of using a combination of styrene–butadiene rubber (SBR) and acrylate polymer to improve the toughness of pervious concrete while keeping its permeability. Single-sized aggregate and no sand were considered in the concrete mixture. Acrylate polymers with different solid content, PH, density, and viscosity were emulsion copolymerized with an SBR polymer. Eleven scenarios with different mix proportions and 220 specimens for compressive strength, flexural strength, flexural stiffness, impact resistance, and fracture toughness tests were selected to evaluate the effects of the copolymer on the toughness of copolymer-modified pervious concrete (CMPC). The studies showed that (1) the influence trend of the copolymers generally varied according to different mechanical indexes; (2) XG–6001 acrylate polymer mainly and comprehensively enhanced the toughness of the CMPC; (3) it was difficult to increase the enhancing property of the XG–6001 acrylate polymer with the growth of its mix proportion; (4) the zero-sand pervious concrete with 90% SBR and 10% XG–6001 acrylate emulsion copolymerization proved to have relatively high toughness. The proposed CMPC holds promising application value in sustainability traffic road construction.