Based on effective medium theory and dielectric resonator theory, we propose the design of reconfigurable all-dielectric metamaterial frequency selective surfaces (FSSs) using high-permittivity ceramics. The FSS is composed of ceramic resonators with different band stop responses under front and side incidences. By mechanically tuning the orientation of the ceramic resonators, reconfigurable electromagnetic (EM) responses between two adjacent stopbands can be achieved. The two broad stopbands originate from the first two resonant modes of the ceramic resonators. As an example, a reconfigurable FSS composed of cross-shaped ceramic resonators is demonstrated. Both numerical and experimental results show that the FSS can switch between two consecutive stopbands in 3.55-4.60 GHz and 4.54-4.94 GHz. The design method can be readily extended to the design of FSSs in other frequencies for high-power applications.