Backdoor attacks on deep neural networks (DNNs) have garnered significant attention, particularly in edge computing applications. Given the complexity and opacity of DNNs, defending against backdoor attacks remains a formidable challenge. To address this, we propose CL-Guard, a dual-network-based defense framework designed to effectively eliminate potential backdoors in models. First, it leverages an inter-layer backpropagation algorithm to quantify each neuron's contribution to model prediction. Next, it constructs a critical neuron set through a recursive hierarchical partitioning method and an adaptive search strategy, identifying neurons critical to model prediction while minimizing the inclusion of backdoor-related neurons. Then, we perform sparse training on the non-critical neuron set, effectively strengthening the weights of critical neurons while disrupting the association between trigger features and backdoor-related neurons. Finally, we design a dual-network architecture that incorporates a fine-grained gradient backpropagation mechanism and dynamic collaborative learning, enabling the model to retain its original accuracy while preventing backdoor reactivation. The experimental results indicate that CL-Guard achieves an average Security Effectiveness Index (SEI) of approximately 95.42\%, representing a 21.23\% improvement over the state-of-the-art FT-SAM method.