We present the hybrid polarized vector optical fields (HP-VOFs) with multi singularities, and find that the purely longitudinal spin angular momentum (SAM) can partially transform into transverse SAM in tight focusing process. The concept of singularity phase is further proposed, providing additional degrees of freedom in modulating polarization configuration on the wave front. After introducing the singularity phase, purely transverse SAM is achieved for the tightly focused HP-VOF with multi singularities, indicating that the singularity phase can play a role as a catalyst to generate the purely transverse SAM in the tight focusing process. This is a new method to achieve purely transverse SAM, which would have potential applications in various areas including chip optical circuitry, optical quantum computing, and optical manipulation.