Nowadays, the nanosandwich structure stands as one of the most promising candidates for nanodevices and nanocomposites (e.g., nanogenerator, nano-energy harvester) due to its superior mechanical properties. The size-dependent response analysis of nanosandwich structure under extreme in-service environment is of great importance for its fabrication and exploitation. This motivates us to study the transient responses of nanosandwich structure subjected to the symmetrical transient thermal and chemical potential shock loads, which are both imposed on its upper and lower bounding surfaces. It is further assumed that thermal contact resistance and diffusional contact impedance at the interface of each two adjacent layers are zero with ideal adhesion. For each isotropic homogeneous elastic layer, the governing equations are formulated in the context of size-dependent generalized thermoelastic diffusion theory and then are solved by using Laplace transformation techniques. The effects of elastic nonlocal parameter, fractional order parameters as well as material characteristic parameters on structural transient responses are also analyzed and discussed. The present study not only provides a comprehensive understanding of the size-dependent thermoelastic diffusion coupling of nanosandwich structure, but also offers basic guidelines for optimal design.