Structured optical fields embedded with polarization singularities (PSs) have attracted extensive attention due to their capability to retain topological invariance during propagation. Many advances in PS research have been made over the past 20 years in the areas of mathematical description, generation and detection technologies, propagation dynamics, and applications. However, one of the most crucial and difficult tasks continues to be manipulating PSs with multiple degrees of freedom, especially in three-dimensional (3D) tailored optical fields. We propose and demonstrate the longitudinal PS lines obtained by superimposing Bessel-like modes with orthogonal polarization states on composite vector optical fields (VOFs). The embedded PSs in the fields can be manipulated to propagate robustly along arbitrary trajectories, or to annihilate, revive, and transform each other at on-demand positions in 3D space, allowing complex PS’ topological morphology and intensity patterns to be flexibly customized. Our findings could spur further research into singular optics and help with applications such as micromanipulation, microstructure fabrication, and optical encryption.