Among many modulation methods, strain engineering is often chosen for nanomaterials to produce tunable band gaps continuously. Inspired by the recently reported two-dimensional material PC3, we explore the tuning of strain on the spin-dependent transport properties of PC3 nanoribbons using the first-principle approach. Surprisingly, strain regulation achieves uninterrupted completely dual-spin polarization over a wide energy range near EF. Analysis reveals that the peculiar transmission spectra arise from the interesting evolution of the band structure, in which strain induces bands to shift and broaden/flatten. This results in triggering the transition of PC3NRs from bandgap-tunable bipolar magnetic semiconductors to spin-gapless semiconductors to ferromagnetic metals or half-metal magnets. Their unique performance demonstrates great potential in spintronics, and our study is expected to provide ideas and theoretical support for the design and application of novel PC3-based spintronic devices in the future.