Hypergraphs are generalized representations of ordinary graphs, which are common in many application areas, including the Internet, bioinformatics, and social networks. The independent set problem is a fundamental research problem in the field of graph analysis. Most of the traditional independent set algorithms are targeted for ordinary graph data, and how to achieve efficient maximum independent set mining on hypergraph data is an urgent problem to be solved. To address this problem, this study proposes a definition of hypergraph independent sets. Firstly, two properties of hypergraph independent set search are analyzed, and then a basic algorithm based on the greedy strategy is proposed. Then a pruning framework for hypergraph approximate maximum independent set search is proposed, i.e., a combination of exact pruning and approximate pruning, which reduces the size of the graph by the exact pruning strategy and speeds up the search by the approximate pruning strategy. In addition, four efficient pruning strategies are proposed in this study, and a theoretical proof of each pruning strategy is presented. Finally, experiments are conducted on 10 real hypergraph data sets, and the results show that the pruning algorithm can efficiently search for hypergraph maximum independent sets that are closer to the real results.