Salt stress is a significant abiotic stress that reduces crop yield and quality globally. In this study, we utilized RNA sequencing (RNA-Seq) to identify differentially expressed genes (DEGs) in response to salt stress induced by gamma-ray irradiation in a salt-tolerant soybean mutant. The total RNA library samples were obtained from the salt-sensitive soybean cultivar Kwangan and the salt-tolerant mutant KA-1285. Samples were taken at three time points (0, 24, and 72 h) from two tissues (leaves and roots) under 200 mM NaCl. A total of 967,719,358 clean reads were generated using the Illumina NovaSeq 6000 platform, and 94.48% of these reads were mapped to 56,044 gene models of the soybean reference genome (Glycine_max_Wm82.a2.v1). The DEGs with expression values were compared at each time point within each tissue between the two soybeans. As a result, 296 DEGs were identified in the leaves, while 170 DEGs were identified in the roots. In the case of the leaves, eight DEGs were related to the phenylpropanoid biosynthesis pathway; however, in the roots, Glyma.03G171700 within GmSalt3, a major QTL associated with salt tolerance in soybean plants, was differentially expressed. Overall, these differences may explain the mechanisms through which mutants exhibit enhanced tolerance to salt stress, and they may provide a basic understanding of salt tolerance in soybean plants.