A systematic study using neutron diffraction and magnetic susceptibility are reported on Mn substituted ferrimagnetic inverse spinel Ti 1−x MnxCo 2 O 4 in the temperature interval 1.6 K ≤ T ≤ 300 K. Our neutron diffraction study reveals cooperative distortions of the T O 6 octahedra in Ti 1−x MnxCo 2 O 4 system for all the Jahn-Teller active ions T = Mn 3+ , Ti 3+ and Co 3+ , having the electronic configurations 3d 1 , 3d 4 and 3d 6 , respectively which are confirmed by the Xray photoelectron spectroscopy. Two specific compositions (x = 0.2 and 0.4) have been chosen in this study because these two systems show unique features such as; (i) Noncollinear Yafet-Kittel type magnetic ordering, and (ii) Weak tetragonal distortion with c/a < 1, in which the apical bond length dc(T B -O) is longer than the equatorial bond length d ab (T B -O) due to the splitting of the eg level of Mn 3+ ions into d x 2 −y 2 and d z 2 . For the composition x = 0.4, the distortion in the T B O 6 octahedra is stronger as compared to x = 0.2 because of the higher content of trivalent Mn. Ferrimagnetic ordering in Ti 0.6 Mn 0.4 Co 2 O 4 and Ti 0.8 Mn 0.2 Co 2 O 4 sets in at 110.3 and 78.2 K, respectively due to the presence of unequal magnetic moments of cations, where Ti 3+ , Mn 3+ , and Co 3+ occupying the octahedral, whereas, Co 2+ sits in the tetrahedral site. For both compounds an additional weak antiferromagnetic component could be observed lying perpendicular to the ferrimagnetic component. The analysis of static and dynamic magnetic susceptibilities combined with the heat-capacity data reveals a magnetic compensation phenomenon (MCP) at T COMP = 25.4 K in Ti 0.8 Mn 0.2 Co 2 O 4 and a reentrant spin-glass behaviour in Ti 0.6 Mn 0.4 Co 2 O 4 with a freezing temperature ∼110.1 K. The MCP in this compound is characterized by sign reversal of magnetization and bipolar exchange bias effect below T COMP with its magnitude depending on the direction of external magnetic field and the cooling protocol. arXiv:2003.09308v1 [cond-mat.str-el]