Deep incomplete multi-view clustering methods can mine patterns of incomplete multi-view data without labels, gaining great attention in various domains. However, current methods are obsessed with aligning view-specific representations from available samples with complete views to learn view-invariant information for missing data recovery, ignoring fruitful view-complementary information beneficial to data imputations. Meanwhile, such the view-invariant learning often leads to the problem of dominant view dependency that models tend to over-rely on views with clear clustering structures and neglect weaker ones, causing a performance bottleneck. Therefore, a content-style disentanglement guided representation learning is proposed for the incomplete multi-view clustering (CSMVC). Specifically, CSMVC designs a view-specific dual-representation learning architecture that extracts view-invariant content representations and view-specific style representations from self-supervised reconstructions of each view with the guidance of the Hilbert schmidt independence criterion. Then, it performs a content-centered style-modulated representation imputation mechanism to infer missing data via fully utilizing inter-view complementary and consistent information. Meanwhile, it devises a cross-view consensus structure mining strategy to capture the clustering structure with intra-cluster compactness and inter-cluster separability from attention-based fusion representations that adaptively aggregate content representations and style representations of each view. Finally, comprehensive experiments show that CSMVC outperforms state-of-the-art methods.