A specially designed metamaterial was investigated wherein the top metasurface was comprised of MgF2-graphene periodic nanopillers formed over an InSb nanolayer. The transmission characteristics of metamaterial was artificially controlled, and the effects due to altering external stimuli, such as thermal ambience, graphene chemical potential and magnetostatic bias, were studied in the 6–15 THz regime. The structure exhibits vanishing transmission with sharp (transmission) minima in certain frequencies, the positions of which essentially depends on the external stimuli. The angular dependence and polarization-insensitive properties were also discussed, apart from the effect of using different numbers of graphene layers in the nanopillers. The results show potential of the metamaterial as sensor due to the thermal, electrical and magnetic variations.