Molecular dynamics simulation is performed to study the phase separation and the glass transition of a binary liquid mixture when the external pressure is increased from 0 to 2.75 GPa. The structure and dynamic characteristics in the glass transition process are calculated. We find that external pressure will promote the phase separation, and make the glass transition temperature increase. The external pressure will make the transition temperature become higher, at which the β relaxation emerge, the time of β relaxation becomes longer, and the diffusibility of the system becomes lower. We first found that in the phase separation liquid microscopic heterogeneity exists during the glass transition.