The recently developed concept of time-varying metamaterials paves the way for advanced methods of electromagnetic property modulation, such as magnet-free isolators, frequency converters, and other nonreciprocal photonic components. Here, we analyze the metamaterial based on the periodically arranged temporally modulated graphene layers via a steplike graphene Fermi level. The material properties are described by the effective medium theory. The electromagnetic wave temporal scattering phenomenon caused by rapid steplike graphene Fermi level switching is considered. It is demonstrated that the frequency of scattered waves increases as the Fermi level grows rapidly and vice versa. The relation between the amplitudes of forward- and backward-scattered waves is found using the Laplace transform technique. The proposed concept allows us to efficiently generate frequency harmonics under instant switching of the graphene Fermi level at a few meV. Our investigation provides a basement for the realization of temporally modulated multilayer structures based on functional tunable materials as power-efficient frequency converters.