Abstract Terrestrial exoplanets around M- and K-type stars are important targets for atmospheric characterization. Such planets are likely tidally locked with the order of spin–orbit resonances (SORs) depending on eccentricity. We explore the impact of SORs on 3D atmospheric dynamics and chemistry, employing a 3D coupled climate-chemistry model to simulate Proxima Centauri b in 1:1 and 3:2 SORs. For a 1:1 SOR, Proxima Centauri b is in the Rhines rotator circulation regime with dominant zonal gradients (global mean surface temperature 229 K). An eccentric 3:2 SOR warms Proxima Centauri b to 262 K with gradients in the meridional direction. We show how a complex interplay between stellar radiation, orbit, atmospheric circulation, and (photo)chemistry determines the 3D ozone distribution. Spatial variations in ozone column densities align with the temperature distribution and are driven by stratospheric circulation mechanisms. Proxima Centauri b in a 3:2 SOR demonstrates additional atmospheric variability, including daytime–nighttime cycles in water vapor of +55% to −34% and ozone (±5.2%) column densities and periastron–apastron water vapor cycles of +17% to −10%. Synthetic emission spectra for the spectral range of the Large Interferometer For Exoplanets fluctuate by up to 36 ppm with the orbital phase angle for a 1:1 SOR due to 3D spatial and temporal asymmetries. The homogeneous atmosphere for the 3:2 SOR results in relatively constant emission spectra and provides an observational discriminant from the 1:1 SOR. Our work emphasizes the importance of understanding the 3D nature of exoplanet atmospheres and associated spectral variations to determine habitability and interpret atmospheric spectra.