Many experiments in modern quantum optics require the implementation of lightweight and near-perfect reflectors for noise reduction and high sensitivity. Another important application of low mass and high reflectivity mirrors is related to the development of solar or laser-driven light sails for acceleration of ultra-light spacecrafts to relativistic velocities. Here, we present numerical results and theoretical analysis of a metasurface mirror consisting of periodically arranged silicon nanospheres embedded in a polymer. In the absence of material losses or disorder, this mirror demonstrates absolute 100% reflection at a single wavelength, which can be tuned by changing nanosphere dimensions or periodicity (for example, by mechanical stretching). We show that high reflectivity can be reached due to electric or magnetic dipole resonant responses of Si nanoparticles in the metasurface. Dependence of mirror reflectivity on surrounding conditions, nanoparticle sizes, and the disorder in the array is studied and discussed. The optimization and simulation procedures presented in this work can be used for the development of other optical devices with functional characteristics determined by the resonant interaction of light with metasurfaces made of nanospheres.