The development of femtosecond lasers has renovated micromachining technology, enabling the microdrilling of transparent materials at high speed. Although effective, this technique is still imperfect because irregular microscopic damage occurs during processing. Several factors in the formation of damage induced by a single laser pulse have been suggested; however, the entire mechanisms of damage formation in the process of drilling are not fully understood. Here we investigated the causes of microscopic damage both by experimentally carrying out laser drilling on chemically strengthened glass samples and by numerically analyzing the propagating stress wave and temperature distribution. We have revealed that the damage at the sidewall and bottom of a generated hole is mainly due to the stress wave, while the damage around the hole entrance is mainly due to relaxation of thermal stress. In particular, we have analyzed these processes quantitatively, demonstrating the time courses of the passage of the stress wave through the material and the temperature distribution generated by the excited electrons. Our analyses are useful in suggesting processing techniques, or suggesting glass materials suitable for laser drilling such as glass with high heat resistance, which may lead to an improvement in the quality of micromachining.