Rare earth metals exhibit strong chemical activity and have many unique properties in the aspects of magnetic susceptibility, photo-absorption, catalytic activity and electrical property. Precious metals have strong chemical stability and great surface-enhanced Raman scattering (SERS) enhancing activity, providing a good platform for detecting SERS signals from molecules. Combining precious metals with rare earth metals could form new composite materials, providing more possibilities for SERS substrates. In this work, the SERS and absorption spectra of the probe molecule adsorbed on scandium-doped silver/copper clusters are theoretically simulated by time-dependent density functional theory. The contributions of charge-transfer (CT) enhancement and electromagnetic enhancement are treated uniformly in calculations based on a short-time approximation for the Raman scattering cross-section, and distinguished by using visualization of electron transitions. The largest Raman enhancement factor of the probe molecule adsorbed on Sc@Cu7 and Sc@Ag7 alloy clusters could reach the order of 105, due to the enhancement of resonance excitation to the CT transition. The factors influencing SERS are systematically investigated, including the composition of the substrate, local chemical environment of the binding site, form of electron transition, oscillator strength of excitation and excitation wavelength.