Existing hypergraph clustering methods typically assume that node attributes are fully available. However, in real-world scenarios, missing node attributes are common due to factors such as data privacy concerns or failures in data collection devices. While some approaches attempt to handle missing attributes in traditional graphs, they are not designed for hypergraphs, which encode higher-order relationships and introduce additional challenges. To bridge this gap, we propose \textbf{H}ypergraph \textbf{C}lustering \textbf{N}etwork with \textbf{P}artial \textbf{A}ttribute \textbf{I}mputation (HCN-PAI). Specifically, we first leverage higher-order neighborhood propagation to impute missing node attributes by minimizing the Dirichlet energy, ensuring smooth feature propagation across the hypergraph. Next, we introduce a hypergraph smoothing preprocessing that efficiently captures structural information, replacing the hypergraph convolution operation, and significantly reducing computational costs. Finally, we design a dual-space projection contrast mechanism, which employs two independent MLPs to encode node representations into two distinct views and enforces consistency at both node and hyperedge levels. Extensive experiments on multiple benchmark datasets validate the effectiveness and superiority of our proposed method.