Photoionization cross section calculations are performed for the ground ([Ne]3s23p63d 2D ) and the first two excited ([Ne]3s23p63d 2D and [Ne]3s23p64s 2S ) states of potassium-like transition metal ions (Sc+2, Ti+3, V+4, Cr+5, Mn+6, Fe+7), along with photoionization calculations for K-like Ca+ ions in the ground ([Ne]3s23p64s 2S ) state and the first two excited ([Ne]3s23p63d 2D and [Ne]3s23p63d 2D ) states. The discrete N-electron final state ion system orbitals are generated using the computer program AUTOSTRUCTURE; 24 configurations are included in the configuration-interaction (CI) calculation for transition metal ions, and 30 configurations for the case of Ca+ ions. The initial and final (N+1)-electron wavefunctions are generated using R-matrix along with photoionization cross sections. In addition to the non-relativistic (LS-coupling) R-matrix, we have used the relativistic (Breit-Pauli) R -matrix method to carry out these calculations to focus on relativistic effects. Relativistic and non-relativistic results are compared to demonstrate the influence of relativistic effects. The prominent 3p → 3d giant resonances are analyzed and identified, and our calculated positions and widths are compared with experimental results for K-like ions such as Ca+, Sc+2 and Ti+3. In the case of lower Z (22  Z  20) ions (Ca+, Sc+2 and Ti+3), the photoionization cross section spectra are dominated by the giant (3p  3d excitation) resonances, while in cases of higher Z (26  Z  23) ions (V+4, Cr+5, Mn+6 and Fe+7), the 3p  3d resonances lie below the ionization threshold, and the cross sections are dominated by 3p53d nd and 3p53d n’s Rydberg series of resonances. Comparison of the Ca+, Sc+2 and Ti3+ results with available theoretical and experimental data shows good agreement.