Enriching the material variation often contributes to the progress of materials science. We have discovered for the first time antiperovskite arsenide SrPd$_{3}$As and revealed a hidden structural and superconducting phase in Sr(Pd$_{1-x}$Pt$_{x}$)$_{3}$As. The Pd-rich samples (0 $\leq$ x $\leq$ 0.2) had the same non-centrosymmetric (NCS) tetragonal structure (a space group of $I41md$) as SrPd$_{3}$P. For the samples with 0.3 $\leq$ x $\leq$ 0.7, a centrosymmetric (CS) tetragonal structure ($P4/nmm$) identical to that of SrPt$_{3}$P was found to appear, accompanied by superconductivity at a transition temperature ($T_\mathrm{c}$) up to 3.7 K. In the samples synthesized with Pt-rich nominal compositions (0.8 $\leq$ x $\leq$ 1.0), Sr$_{2}$(Pd,Pt)$_{8-y}$As$_{1+y}$ with an intergrowth structure (CS-orthorhombic with Cmcm) was crystallized. The phase diagram obtained for Sr(Pd,Pt)$_{3}$As was analogous to that of (Ca,Sr)Pd$_{3}$P in that superconductivity ($T_\mathrm{c}$ $\geq$ 2 K) occurred in the CS phases induced by substitutions to the NCS phases. This study indicates the potential for further material variation expansion and the importance of elemental substitutions to reveal hidden phases in related antiperovskites.