In this paper, we proposes the construction methods of sliced space-filling design when the quantitative factors are mixture components. Leveraging the representative points framework for distribution and energy distance decomposition theory, this paper proposes three methods for constructing sliced representative points and establishes their distributional convergence. Furthermore, one-shot and sequential algorithms for generating sliced space-filling mixture design for experiments with process variables are presented with convergence proofs. Compared to existing methods, the proposed sliced space-filling mixture design exhibits greater flexibility in subdesign run sizes and broader applicability to constrained experimental regions. Moreover, numerical results confirm its marked advantages in both space-filling performance and predictive accuracy.