The automatic segmentation of cardiac magnetic resonance (MR) images is the basis for the diagnosis of cardiac-related diseases. However, the segmentation of cardiac MR images is a challenging task due to the inhomogeneity of MR images intensity distribution and the unclear boundaries between adjacent tissues. In this paper, we propose a novel multiresolution mutual assistance network (MMA-Net) for cardiac MR images segmentation. It is mainly composed of multibranch input module, multiresolution mutual assistance module, and multilabel deep supervision. First, the multibranch input module helps the network to extract local and global features more pertinently. Then, the multiresolution mutual assistance module implements multiresolution feature interaction and progressively improves semantic features to more completely express the information of the tissue. Finally, the multilabel deep supervision is proposed to generate the final segmentation map. We compare with state-of-the-art medical image segmentation methods on the medical image computing and computer-assisted intervention (MICCAI) automated cardiac diagnosis challenge datasets and the MICCAI atrial segmentation challenge datasets. The mean dice scores of our method in the left atrium, right ventricle, myocardium, and left ventricle are 0.919, 0.920, 0.881, and 0.960, respectively. The analysis of evaluation indicators and segmentation results shows that our method achieves the best performance in cardiac magnetic resonance images segmentation.