In order to better understand the dynamic response and failure modes of rock slopes containing weak interlayers subjected to earthquake excitation, a series of numerical simulations were carried out using the continuum-discontinuum element method (CDEM), considering the influence of seismic amplitude and weak interlayers inclination. The seismic response characteristics of slopes were systematically analyzed according to the waveform characteristics, amplification effect, equivalent crack ratio, etc. The numerical results show that the acceleration waveform characteristics and peak ground displacement (PGD) amplification coefficient have good correspondence with the dynamic failure process of landslides. Comprehensive analysis of waveform characteristics and PGD amplification coefficient can determine the damage time, damage location, and damage degree of landslides. The landslide process can be divided into three stages according to the equivalent crack ratio: rapid generation of a large number of microcracks, expansion and aggregation of microcracks, and penetration of micro-cracks and the formation of slip surfaces. The equivalent crack ratio provides a new idea for evaluating slope stability. In addition, under the combination of different amplitudes and weak interlayers, these earthquake-induced landslides exhibit different failure modes: the failure of the gentle-dip slope is mainly local rockfall; The mid-dip and steep-dip slopes with small amplitudes experience “tensile cracking-slip-collapsing” failure; The steep-dip slopes under strong earthquake failed in the form of “tensile cracking-slip-slope extrusion-collapsing”. The research results are of great significance for a deeper understanding of the formation mechanism of rock landslides with weak interlayers and the prevention of such landslide disasters.