High-$Q$ deformed silica microsphere cavities are fabricated by short ${\mathrm{CO}}_2$ laser pulses, where the deformation is well controlled by adjusting the intensity and number of pulses. Using this method, directional emission from whispering-gallery mode (WGM) with a high quality factor of ${10}^7$ in these microspheres is achieved, and a transition from two-directional to single-directional emission is observed. Such concentrated directional emission and high-$Q$ of WGMs show high potential for future studies of the chaotic ray dynamics in deformed microcavity and cavity quantum electrodynamics and optomechanics.