Invention of DNA origami has transformed the fabrication and application of biological nanomaterials. In this review, we discuss DNA origami nanoassemblies according to their four fundamental mechanical properties in response to external forces: elasticity, pliability, plasticity and stability. While elasticity and pliability refer to reversible changes in structures and associated properties, plasticity shows irreversible variation in topologies. The irreversible property is also inherent in the disintegration of DNA nanoassemblies, which is manifested by its mechanical stability. Disparate DNA origami devices in the past decade have exploited the mechanical regimes of pliability, elasticity, and plasticity, among which plasticity has shown its dominating potential in biomechanical and physiochemical applications. On the other hand, the mechanical stability of the DNA origami has been used to understand the mechanics of the assembly and disassembly of DNA nano-devices. At the end of this review, we discuss the challenges and future development of DNA origami nanoassemblies, again, from these fundamental mechanical perspectives.