Fundamental understanding of the climate responses to solar variability is obscured by the large and complex climate variability. This long-standing issue is addressed here by examining climate responses under an extreme solar minimum (ESM) scenario, obtained by making the sun void of all magnetic fields. It is used to drive a whole atmosphere climate model with coupled ocean. The simulations reveal robust responses in the coupled climate system, and elucidate similarities and differences of responses to bottom-up and top-down forcing. Planetary waves (PWs) play a key role in both regional climate and the mean circulation changes. Responses of the largest scale PW during NH and SH winters differ, leading to hemispheric differences in the interplay between dynamical and radiative processes. The analysis exposes remarkable general similarities between climate responses in ESM simulations and those under nominal solar minimum conditions, even though the latter may not appear to be statistically significant.