Graph-level clustering remains a pivotal yet formidable challenge in graph learning. Recently, the integration of deep learning with representation learning has demonstrated notable advancements, yielding performance enhancements to a certain degree. However, existing methods suffer from at least one of the following issues: 1. the original graph structure has noise, and 2. during feature propagation and pooling processes, noise is gradually aggregated into the graph-level embeddings through information propagation. Consequently, these two limitations mask clustering-friendly information, leading to suboptimal graph-level clustering performance. To this end, we propose a novel Dual Boost-Driven Graph-Level Clustering Network (DBGCN) to alternately promote graph-level clustering and filtering out interference information in a unified framework. Specifically, in the pooling step, we evaluate the contribution of features at the global and optimize them using a learnable transformation matrix to obtain high-quality graph-level representation, such that the model's reasoning capability can be improved. Moreover, to enable reliable graph-level clustering, we first identify and suppress information detrimental to clustering by evaluating similarities between graph-level representations, providing more accurate guidance for multi-view fusion. Extensive experiments demonstrated that DBGCN outperforms the state-of-the-art graph-level clustering methods on six benchmark datasets.