Optical parametric chirped-pulse amplification (OPCPA) is a promising approach for generating intense vortex pulses over a broad spectrum. However, its intrinsic parametric superfluorescence (PSF) noise significantly degrades the spatial and temporal contrast of the amplified vortex pulses. Here, we investigate the PSF evolution dynamics during OPCPA of ultrafast vortex pulses and propose three effective strategies to suppress PSF. Our findings indicate that strong vortex seeding can effectively suppress PSF overlapping spatially and temporally with the vortex, but it fails to suppress PSF near the vortex singularity. After focusing, the PSF near the singularity tends to spread into a larger spot than the vortex, allowing for its removal through a far-field spatial aperture. Alternatively, employing a vortex pump can completely prevent such PSF. These research results offer valuable insights for the development of high-contrast vortex OPCPA systems.