The mechanical properties and workability of manufactured sand reactive powder concrete (RPC) mixed with steel and basalt fibers were studied using the response surface method. The central composite design was used to explore the 7-day and 28-day compressive strength, flexural strength, and workability of different amounts of mixed fiber-manufactured sand RPC. Results showed that when the steel fiber content was less than 2.5%, mixing basalt fibers can significantly improve the flexural strength and flexural-compressive ratio of RPC. The relationship equations of the two fibers with the 28-day compressive strength, flexural strength, and flexural-compressive ratio of the manufactured sand RPC were obtained through the response surface model. The model proved to be reliable according to the analysis of variance. The content of the two fibers was optimized by multiobjective optimization technology, and the optimal content of the mixed fiber-manufactured sand RPC under standard curing conditions was verified.