As part of the SAGES Legacy Unifying Globulars and GalaxieS (SLUGGS) survey, we stack 1137 Keck DEIMOS (Deep Imaging Multi-Object Spectrograph) spectra of globular clusters from 10 galaxies to study their stellar populations in detail. The stacked spectra have median signal-to-noise ratios of ∼90 Å−1. Besides the calcium triplet, we study weaker sodium, magnesium, titanium and iron lines as well as the Hα and higher order Paschen hydrogen lines. In general, the stacked spectra are consistent with old ages and a Milky Way-like initial mass function. However, we see different metal line index strengths at fixed colour and magnitude, and differences in the calcium triplet–colour relation from galaxy to galaxy. We interpret this as strong evidence for variations in the globular cluster colour–metallicity relation between galaxies. Two possible explanations for the colour–metallicity relation variations are that the average ages of globular clusters vary from galaxy to galaxy or that the average abundances of light elements (i.e. He, C, N and O) differ between galaxies. Stacking spectra by magnitude, we see that the colours become redder and metal line indices stronger with brighter magnitudes. These trends are consistent with the previously reported ‘blue tilts’ being mass–metallicity relations.