Topotactic modification, by both oxidation and reduction, of the composition, structures, and magnetic properties of the layered oxychalcogenides Sr4Mn3O7.5Cu2Ch2 (Ch=S, Se) is described. These Mn3+ compounds are composed of alternating perovskite-type strontium manganese oxide slabs separated by anti-fluorite-type copper chalcogenide layers and are intrinsically oxide deficient in the central layer of the perovskite slabs. The systems are unusual examples of perovskite-related compounds that may topotactically be both oxidized by fluorination and reduced by deintercalation of oxygen from the oxide-deficient part of the structure. The compounds exhibit antiferromagnetic ordering of the manganese magnetic moments in the outer layers of the perovskite slabs, while the other moments, in the central layers, exhibit spin-glass-like behavior. Fluorination has the effect of increasing the antiferromagnetic ordering temperature and the size of the ordered moment, whereas reduction destroys magnetic long-range order by introducing chemical disorder which leads to both further disorder and frustration of the magnetic interactions in the manganese oxide slab.