We investigate the low-energy scattering and femtoscopic correlation functions of the $d-\Lambda$, $d-\Sigma$, and $d-\Xi$ systems within a microscopic folding approach. The effective deuteron–hyperon interactions are constructed by folding the HAL-QCD hyperon–nucleon potentials with the deuteron wave function, while the spin and isospin structures are treated through Wigner-$6j$ recoupling coefficients. Using the resulting interactions, we calculate the scattering parameters and momentum correlation functions for all spin channels. No bound states are found for the $d-\Lambda$, $d-\Sigma$, or $d-\Xi$ systems. Nevertheless, the $d-\Lambda$ correlation exhibits a pronounced low-momentum enhancement associated with a large scattering length and a near-threshold pole, whereas the $d-\Sigma$ correlation is suppressed by its predominantly repulsive interaction. The neutral $d-{\Xi }^0$ system shows only a moderate enhancement, while the charged $d-{\Xi }^{-}$ correlation is strongly amplified by the attractive Coulomb interaction. We further investigate feed-down effects from ${\Sigma }^0$, $\Sigma (1385)$, and $\Xi$ decays using Monte Carlo response matrices and demonstrate that these decays clearly modify the observable $d-\Lambda$ correlation. Our results provide quantitative predictions for future femtoscopic measurements and establish deuteron–hyperon correlations as a sensitive probe of hyperon–nucleus interactions.