Existing deep learning methods handle magnetic resonance (MR) image reconstruction and segmentation as individual task instead of considering their correlations. However, the simple concatenation of the reconstruction and segmentation networks can compromise the performances on both tasks due to the differences in optimization. This paper develops a multi-task deep learning method for the combinatorial reconstruction and segmentation of MR images using an improved teacher forcing network training strategy. The newly designed teacher forcing scheme guides multi-task network training by iteratively using intermediate reconstruction outputs and fully sampled data to avoid error accumulation. We compared the effectiveness of the proposed method with six state-of-the-art methods on an open dataset and an in vivo in-house dataset. The experimental results show that compared to other methods, the proposed method possesses encouraging capabilities to achieve better image reconstruction quality and segmentation accuracy while co-optimizing MR image reconstruction and segmentation simultaneously.