Specific energy consumption is an important indicator for a better understanding of the machinability of materials. The present study aims to estimate the specific energy consumption for abrasive metal cutting with ultra-thin discs at comparatively low and medium feed rates. Using an experimental technique, the cutting power was measured at four predefined feed rates for S235JR, intermetallic Fe-Al(40%), and C45K with different thermal treatments. The variation in the specific energy consumption with the material removal rate was analyzed through an empirical model, which enabled us to distinguish three phenomena of energy dissipation during material removal. The thermal treatment and mechanical properties of materials have a significant impact on the energy consumption pattern, its corresponding components, and cutting power. Ductile materials consume more specific cutting energy than brittle materials. The specific cutting energy is the minimum energy required to remove the material, and plowing energy is found to be the most significant phenomenon of energy dissipation.