Magnetic properties as well as the specific heat of the spin-dimer system La 2 Ru 1−y Mn y O 5 were investigated for manganese concentrations 0 y 0.25. The magnetic (dc) susceptibility of the unsubstituted (y = 0) system shows a steplike decrease close to 160 K reflecting a magnetostructural transition into a dimerized ground state. With increasing manganese concentration this behavior (typical for singlet formation) becomes continuously suppressed and the susceptibility bears the signatures of the emergence of new magnetic ground states. The high-temperature Curie-Weiss susceptibility can be described by Ru 4+ (S = 1) and Mn 4+ (S = 3 2 ) spin moments, with a dramatic decrease of the Curie-Weiss temperatures by almost 30% close to y = 0.1, indicating significant changes in the average mean magnetic exchange. Field-cooled and zero-field-cooled experiments as well as ac-susceptibility measurements provide clear evidence for the formation of a spin-glass state, well below the characteristic dimerization temperature. The relaxation dynamics can be described by a Vogel-Fulcher-Tammann behavior and indicates high fragility when characterized in terms of glassy dynamics of canonical supercooled liquids. Additional electron-spin resonance experiments indicate different spin-glass regimes and a rather dynamic nature of the dimerized phase. In the Mn-substituted compounds, a linear contribution to the heat capacity at low temperatures can be ascribed to the spin-glass formation. With increasing manganese concentration, the anomaly in the specific heat caused by the spin-singlet formation is shifted to lower temperatures and becomes continuously suppressed and smeared out. On the basis of these results, we propose a (y,T )-phase diagram indicating the competition of the spin-glass and the dimerized states. We stress the similarities with doped CuGeO 3 , the canonical inorganic spin-Peierls system.