The 21-cm signal from the epoch of cosmic dawn prior to reionization consists of a promising observable to gain new insights into the dark matter (DM) sector. In this paper, we investigate its potential to constrain mixed (cold+noncold) dark matter scenarios that are characterized by the noncold DM fraction (fnCDM) and particle mass (mnCDM). As noncold DM species, we investigate both a fermionic (sterile neutrino) and a bosonic (ultralight axion) particle. We show how these scenarios affect the global signal and the power spectrum using a halo-model implementation of the 21-cm signal at cosmic dawn. Next to this study, we perform an inference-based forecast study based on realistic mock power spectra from the Square Kilometre Array (SKA) telescope. Assuming inefficient, yet nonzero star formation in minihaloes (i.e., haloes with mass below 108 M), we obtain stringent constraints on both mnCDM and fnCDM that go well beyond current limits. Regarding the special case of fnCDM1, for example, we find a constraint of mnCDM>15 keV (thermal mass) for fermionic DM and mnCDM>2×10−20 eV for bosonic DM. For the opposite case of dominating cold DM, we find that at most 1% of the total DM abundance can be made of a hot fermionic or bosonic relic. All constraints are provided at the 95% confidence level.