The ability of a material to adopt multiple structures, known as polymorphism, is a fascinating natural phenomenon. Various polymorphs with unusual properties are routinely synthesized by compression under positive pressure. However, changing a material's structure by applying tension under negative pressure is much more difficult. We show how negative-pressure polymorphs can be synthesized by mixing materials with different crystal structures-a general approach that should be applicable to many materials. Theoretical calculations suggest that it costs less energy to mix low-density structures than high-density structures, due to less competition for space between the atoms. Proof-of-concept experiments confirm that mixing two different high-density forms of MnSe and MnTe stabilizes a Mn(Se,Te) alloy with a low-density wurtzite structure. This Mn(Se,Te) negative-pressure polymorph has 2× to 4× lower electron effective mass compared to MnSe and MnTe parent compounds and has a piezoelectric response that none of the parent compounds have. This example shows how heterostructural alloying can lead to negative-pressure polymorphs with useful properties-materials that are otherwise nearly impossible to make.