Context. The evolution of massive stars depends on several physical processes and parameters. Metallicity and rotation are among the most important, but their quantitative effects are not well understood.Aims. To complement our earlier study on main-sequence stars, we study the evolutionary and physical properties of evolved O stars in the Small Magellanic Cloud (SMC). We focus in particular on their surface abundances to further investigate the efficiency of rotational mixing as a function of age, rotation, and global metallicity.Methods. We analysed the UV and optical spectra of 13 SMC O-type giants and supergiants using the stellar atmosphere code CMF-GEN to derive photospheric and wind properties. We compared the inferred properties to theoretical predictions from evolution models. For a more comprehensive analysis, we interpret the results together with those we previously obtained for O-type dwarfs.Results. Most dwarfs of our sample lie in the early phases of the main sequence. For a given initial mass, giants are farther along the evolutionary tracks, which confirms that they are indeed more evolved than dwarfs. Supergiants have higher initial masses and are located past the terminal-age main-sequence in each diagram. We find no clear trend of a mass discrepancy, regardless of the diagram that was used to estimate the evolutionary mass. Surface 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. Above about 30 M , more massive stars are on average more chemically enriched at a given evolutionary phase. Below 30 M , the trend vanishes. This is qualitatively consistent with evolutionary models. A principal component analysis of the abundance ratios for the whole (dwarfs and evolved stars) sample 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, for some objects, a stronger braking and/or more efficient mixing is required.