The reaction D-2(+) + H-2 --> D2H+ + H*(n > 1) or H2D+ + D*(n > 1) is studied experimentally at a relative collision energy of 20 eV. The ionic products are angle and energy analyzed in coincidence with the excited atomic products. The latter are detected by the radiation they emit, possibly after quenching in case of metastable atoms. The contour diagrams obtained for the intensity of the D2H+ or H2D+ products as functions of their center-of-mass scattering angle and velocity show the presence of these two products, with a predominance of the former. These products are essentially found in low vibrational levels and the correlated atoms are observed predominantly in n = 2 states; the 2s to 2p cross section ratio is found to be nearly equal to 0.35. That the considered reaction exists was actually predicted on the basis of its analogy with the reaction He+ --> H-2 --> HeH+ + H*(n > 1). The main features of the two reactions are compared. The mechanism of the D-2(+) --> H-2 reaction is explained using an adaptation of the interpretation framework proposed by Dhuicq et al. [Chem. Phys. 206, 139 (1996)] for the He+ + H-2 reaction. It involves energy level promotion, diabatic potential energy surface crossings and related electron transitions, charge transfer, and proton transfer. The discussion shows that the occurrence of this reaction and some of its characteristics stem from the Franck-Condon vibrational distribution of the D2H+ reactant ions and especially to the corresponding distribution of bond distances.