Quality-Diversity (QD) algorithms, as a subset of evolutionary algorithms, have emerged as a powerful optimization paradigm with the aim of generating a set of high-quality and diverse solutions. Although QD has demonstrated competitive performance in reinforcement learning, its low sample efficiency remains a significant impediment for real-world applications. Recent research has primarily focused on augmenting sample efficiency by refining selection and variation operators of QD. However, one of the less considered yet crucial factors is the inherently large-scale issue of the QD optimization problem. In this paper, we propose a novel Cooperative Coevolution QD (CCQD) framework, which decomposes a policy network naturally into two types of layers, corresponding to representation and decision respectively, and thus simplifies the problem significantly. The resulting two (representation and decision) subpopulations are coevolved cooperatively. CCQD can be implemented with different selection and variation operators. Experiments on several popular tasks within the QDAX suite demonstrate that an instantiation of CCQD achieves approximately a 200% improvement in sample efficiency.