SrTi0.5Mn0.5O3 (STMO) is a chemically disordered perovskite having random distribution of Ti and Mn over 1b site. Striking discrepancies about the structural and magnetic properties of STMO demands detailed analysis which is addressed. To explore the magnetic ground state of STMO, static and dynamic magnetic properties were studied over a broad temperature range (2-300 K). The dc, ac magnetization show a cusp like peak at Tf ~ 14 K, which exhibits field and frequency dependence. The thermoremanent magnetization is characterized by using stretched exponential function and characteristic time suggests the existence of spin clusters. Also the other features observed in magnetic memory effect, muon spin resonance/rotation and neutron powder diffraction confirm the existence of cluster spin glass state in STMO, rather than the long range ordered ground state. Intriguingly, the observed spin relaxation can be attributed to the dilute magnetism due to non-magnetic doping at Mn-site and competing antiferromagnetic and ferromagnetic interactions resulting from the site disorder.