Laser cutting of thick diamond films is studied using a low-power(10 W) copper vapor laser. Due to the existence of the saturation depth in laser cutting, thick diamond films are not easily cut by low-power lasers. In this study, we have adopted a low thermalconductivity underlayer of alumina and a heating stage (up to 500$^{circ}C$ in air) to prevent the laser energy from consuming-out and, in turn, enhance the cutting efficiency. Aspect ratio increases twice fromm 3.5 to 7 when the alumina underlayer used. Adopting a heating stage also increases aspect ratio and more than 10 is obtained at higher temperatures than 400$^{circ}C$. These results show that thick diamond films can be cut, with low-power lasers, simply by modifying the thermal property of underlayer.