An analytical expression for the half-plane diffraction of off-axis phase singularity beams based on Gaussian intensity profile is derived, which enables us to study the propagation dynamics of off-axis phase singularities in detail. It is shown that the half-plane screen diffraction, off-axis displacement and propagation distance affect the propagation behavior and spatial distribution of phase singularities. By varying the off-axis displacement and propagation distance, the creation, shift and annihilation of phase singularities in the diffraction field may appear.