We study the evolutionary and physical properties of evolved O stars in the Small Magellanic Cloud (SMC), with a special focus on their surface abundances to investigate the efficiency of rotational mixing as a function of age, rotation and global metallicity. We analyse the UV + optical spectra of thirteen SMC O-type giants and supergiants, using the stellar atmosphere code CMFGEN to derive photospheric and wind properties. We compare the inferred properties to theoretical predictions from evolution models. For a more comprehensive analysis, we interpret the results together with those we obtained for O-type dwarfs in a former study. Most dwarfs lie in the early phases of the main-sequence. For a given initial mass, giants are farther along the evolutionary tracks, confirming that they are more evolved than dwarfs. Supergiants have higher initial masses and are located past the terminal age main-sequence. We find no clear trend of a mass discrepancy, regardless of the diagram that was used to estimate the evolutionary mass. CNO abundances are consistent with nucleosynthesis from the CNO cycle. Comparisons to theoretical predictions reveal that the initial mixture is important when the observed trends in the N/C versus N/O diagram are to be reproduced. A trend for stronger chemical evolution for more evolved objects is observed. More massive stars, are on average, more chemically enriched at a given evolutionary phase, qualitatively consistent with evolutionary models. Abundance ratios supports the theoretical prediction that massive stars at low metallicity are more chemically processed than their Galactic counterparts. Finally, models including rotation generally reproduce the surface abundances and rotation rates when different initial rotational velocities are considered. Nevertheless, there are objects for which a stronger braking and/or more efficient mixing is required.