The exponential growth of global data leads to the problem of insufficient data storage capacity. DNA storage can be an ideal storage method due to its high storage density and long storage time. However, the DNA storage process is subject to unavoidable errors that can lead to increased cluster redundancy during data reading, which in turn affects the accuracy of the data reads. This paper proposes a dynamically updated hash index (DUHI) clustering method for DNA storage, which clusters sequences by constructing a dynamic core index set and using hash lookup. The proposed clustering method is analyzed in terms of overall reliability evaluation and visualization evaluation. The results show that the DUHI clustering method can reduce the redundancy of more than 10% of the sequences within the cluster and increase the reconstruction rate of the sequences to more than 99%. Therefore, our method solves the high redundancy problem after DNA sequence clustering, improves the accuracy of data reading, and promotes the development of DNA storage.