One of the primary parts of a closed Brayton cycle that uses a helium–xenon mixture as the working medium is a centrifugal compressor. Nowadays, there has been minimal research on the theoretical underpinnings and design procedures of a helium–xenon mixture centrifugal compressors, and the internal flow mechanisms remain poorly understood. In this study, we present a redesign of the 15 g/mol helium–xenon centrifugal compressor originally developed by Bruno M, utilizing a helium–xenon mixture as the working fluid to enhance compressor performance and facilitate an in-depth analysis of the internal flow dynamics. The findings indicate a significant expansion of the stable operating range of the redesigned compressor under identical outlet conditions, with a 33.27% increase in flow margin and substantial improvements in the pressure ratio. Furthermore, under consistent inlet conditions, at an operational flow rate of 0.8657 kg/s, the redesigned compressor exhibits a pressure ratio that is 2.11% greater than that of the original design, along with a variable efficiency increase of 1.1%.