The competition mechanism between the slip motions and cleavage fractures is related to the anisotropy of deformation behaviors, which is essential to manufacture complex optical components. To identify competition mechanism between the slip motions and cleavage fractures and reveal the anisotropy of deformation and damage behaviors of MgF2 crystals, the nanoindentation tests were systematically conducted on different crystal planes. In addition, the stress induced by the nanoindentation was developed and decomposed along the slip systems and cleavage planes, and cleavage factors and Schmid factors were calculated. The stress, cleavage factors and Schmid factors indicated that the activation degree of the slip motions and cleavage fractures determined the indentation morphologies. Under the same indentation conditions, the nanoindentation of the (001) crystal plane activated most slip motions, so the plastic deformation is most prone to occur on this crystal plane. The nanoindentation of the (010) crystal plane activated less slip motions and most cleavage fractures, resulting in the severest brittle fractures on the (010) crystal plane. The theoretical results consisted well with the experimental results, which provides the theoretical guidance to the low-damage manufacturing of MgF2 components.