We report studies of the complex magnetic ordering, pressure-induced magnetic properties, large exchange bias (EB), spin-glass (SG), critical behavior, and electron spin resonance (ESR) in spinel Co₂TiO₄. The magnetic compensation behavior occurs in the vicinity of the compensation temperature T_comp ∼ 32.5 K (defined as the susceptibility χ_ZFC = χ_FC = 0), which can be attributed to the behavior that the magnetization of two bulk sublattices balances each other completely. The nature of this unusual case is demonstrated by the spin direction upon applied field and A–B sublattice (site) coupling. Specifically, the values of exchange integrals J_AA and J_BB play a crucial role at lower and higher temperatures, respectively. It is prominent that intrinsic coercivity H_cj increases by 168% at a pressure of 1000 MPa, from which we illustrate the antiferromagnetic (AFM) transition based on magnetic hysteresis loops M(H) and temperature dependent magnetization M(T) curves. The SG behavior of Co₂TiO₄ is confirmed by a series of reliable measurements and fitting parameters (τ₀, zv), and a large EB field is also found through the asymmetry in the M(H) curve. Besides, the critical behavior of Co₂TiO₄ is studied initially in our present work, and the critical exponents (β, γ, and δ) indicate long-range ferromagnetic (FM) coupling accompanied by a short-range interaction in Co₂TiO₄.