Patient survival prediction based on gigapixel whole-slide histopathological images (WSIs) has become increasingly prevalent in recent years. A key challenge of this task is achieving an informative survival-specific global representation from those WSIs with highly complicated data correlation. This paper proposes a multi-hypergraph based learning framework, called "HGSurvNet," to tackle this challenge. HGSurvNet achieves an effective high-order global representation of WSIs via multilateral correlation modeling in multiple spaces and a general hypergraph convolution network. It has the ability to alleviate over-fitting issues caused by the lack of training data by using a new convolution structure called hypergraph max-mask convolution. Extensive validation experiments were conducted on three widely-used carcinoma datasets: Lung Squamous Cell Carcinoma (LUSC), Glioblastoma Multiforme (GBM), and National Lung Screening Trial (NLST). Quantitative analysis demonstrated that the proposed method consistently outperforms state-of-the-art methods, coupled with the Bayesian Concordance Readjust loss. We also demonstrate the individual effectiveness of each module of the proposed framework and its application potential for pathology diagnosis and reporting empowered by its interpretability potential.