Biofabrication of tissues requires sourcing appropriate combinations of cells, and then arranging those cells into a functionally-useful construct. Recently, organoids with diverse cell populations have shown great promise as building blocks from which to assemble more complex structures. However, organoids typically adopt spherical or uncontrolled morphologies, which intrinsically limit the tissue structures that can be produced using this bioassembly technique. Here, we develop microfabricated smart hydrogel platforms in thermoresponsive poly(N-isopropylacrylamide) to compressively mold microtissues such as spheroids or organoids into customized forms, on demand. These Compressive Hydrogel Molders (CHyMs) compact at cell culture temperatures to force loaded tissues into a new shape, and then expand to release the tissues for downstream applications. As a first demonstration, breast cancer spheroids were biaxially compacted in cylindrical cavities, and uniaxially compacted in rectangular ones. Spheroid shape changes persisted after the tissues were released from the CHyMs. We then demonstrate long-term molding of spherical brain organoids in ring-shaped CHyMs over one week. Fused bridges formed only when brain organoids were encased in Matrigel, and the resulting ring-shaped organoids expressed tissue markers that correspond with expected differentiation profiles. These results demonstrate that tissues differentiate appropriately even during long-term molding in a CHyM. This platform hence provides a new tool to shape pre-made tissues as desired, via temporary compression and release, allowing an exploration of alternative organoid geometries as building blocks for bioassembly applications.