Abundant phenomena in CoCr2-xMnxO4 (x = 0 ~ 2) samples such as magnetic compensation, magnetostriction and exchange bias effect have been observed and investigated in this work. A structure transition from cubic to tetragonal symmetry has been found in the samples with x around 1.4. It has shown that the doped Mn3+ ions initially occupy the A (Co) sites when x < 0.2, and then mainly take the B1 (Cr) sites. This behavior results in a role conversion of magnetic contributors, and thus a magnetic compensation between two competitively magnetic sublattices at the composition near x = 0.5. Furthermore, temperature compensation has also been found in the samples with x = 0.5 and 0.6, with the compensation temperature in the range of 45 ~ 75 K. The Mn-doping also changes the frustration degree and modulates the exchange interaction in this system, and thus prevents the formation of long range conical order of spins. Therefore, the magnetoelectric transition temperature at 23 K in CoCr2O4 is shifted to lower temperature with increased dopants. The magnetostriction effect in this Cobalt spinel system has been considered for the first time. The strain has a maximum value of about 240 ppm at x = 0.2 and shows the similar tendency as the compensation behaviors. Additionally, the exchange bias effect observed in the samples with x < 0.5 shows a negative value under low cooling field for x = 0.5.