We have monitored the Didymos–Dimorphos binary asteroid in spectropolarimetric mode in the optical range before and after the DART impact. The ultimate goal was to obtain constraints on the characteristics of the ejected dust for modeling purposes. Before impact, Didymos exhibited a linear polarization rapidly increasing with phase angle, reaching a level of ∼5% in the blue and ∼4.5% in the red. The shape of the polarization spectrum was anticorrelated with that of its reflectance spectrum, which appeared typical of an S-class asteroid. After impact, the level of polarization dropped by about 1 percentage point (pp) in the blue band and about 0.5 pp in the red band, then continued to linearly increase with phase angle, with a slope similar to that measured prior to impact. The polarization spectra, once normalized by their values at an arbitrary wavelength, show very little or no change over the course of all observations before and after impact. The lack of any remarkable change in the shape of the polarization spectrum after impact suggests that the way in which polarization varies with wavelength depends on the composition of the scattering material, rather than on its structure, be this a surface or a debris cloud.