Machinability of LAM(Laser Assisted Machining) has been studied for ceramics such as $Al_2O_3$, $Si_3_N4$ and $ZrO_2$ by $CO_2$ laser. It was possible to remove ceramics by PCBN tool because material became softening and deterioration by local laser beam irradiation. The advantage of LAM is the ability to produce larger material removal rates and tool life. But, for cutting of $Al_2O_3$ and $ZrO_2$, stage of laser power control was needed owing to thermal shock with high temperature of workpiece by laser power. And when $Si_3N_4$ was machined by LAM, $N_2$ gas spouted from surface of one cause of high temperature. Characteristics of LAM were analyzed using pyrometer, dynamometer, SEM and EDS to measure temperature of workpiece surface, cutting force, variation of machining surface and structure of lattice respectively. As the result of this study, it was found that machinability of LAM for ceramics in $CO_2$ laser and mechanism of LAM was different according to the kind of ceramics because of properties of materials.