The present paper investigates the magnetic and magnetoelectric properties of Bi2Ir2-xMnxO7 compounds with respect to the degree of Mn doping denoted by x. It is found that the antiferromagnetic (AFM) interactions are initially enhanced with increasing x, but are then weakened with further increases in x. These findings are explained on the basis of the competition among AFM Ir-Ir, AFM Ir-Mn, and ferromagnetic Mn-Mn interactions. In addition, the electric transport properties at the temperature range studied present a metal-insulator transition in the range 0.05 <= x <= 0.15, while an insulating state occurs for x > 0.15 because of electron localization. At low temperatures, a small positive magnetoresistance (MR) effect is observed for x = 0, whereas a negative MR effect is observed for all Mn-doped samples. The 3d-5d electron interactions play a dominant role in determining the magnetic properties of the doped samples.