Commonsense Knowledge Graphs (CSKGs) are crucial for commonsense reasoning, yet constructing them through human annotations can be costly. As a result, various automatic methods have been proposed to construct CSKG with larger semantic coverage. However, these unsupervised approaches introduce spurious noise that can lower the quality of the resulting CSKG, which cannot be tackled easily by existing denoising algorithms due to the unique characteristics of nodes and structures in CSKGs. To address this issue, we propose Gold (Global and Local-aware Denoising), a denoising framework for CSKGs that incorporates entity semantic information, global rules, and local structural information from the CSKG. Experiment results demonstrate that Gold outperforms all baseline methods in noise detection tasks on synthetic noisy CSKG benchmarks. Furthermore, we show that denoising a real-world CSKG is effective and even benefits the downstream zero-shot commonsense question-answering task. Our code and data are publicly available at https://github.com/HKUST-KnowComp/GOLD.