We theoretically investigate the electron dynamics in Ne atoms involving core-excited states through the Ramsey scheme with a pair of time-delayed x-ray pulses. Irradiation of Ne atoms by the ∼1 femtosecond x-ray pulse simultaneously populates two core-excited states, and an identical but time-delayed x-ray pulse probes the dynamics of the core-excited electron wave packet which is subject to the resonant Auger decay. The energy-integrated total Auger electron yield and energy-resolved Auger electron spectra in the time domain show periodic structures due to the temporal evolution of the wave packet, from which we can obtain the counterpart in the frequency domain through the Fourier transformation. The Auger electron energy spectra in the time as well as frequency domains show the interference patterns between the two Auger electron wave packets released into the continuum from the superposition of two core-excited states at different times. These spectra are important to clarify the individual contribution of the different Auger decay channels upon core excitation by the x-ray pulse.