In cross-lingual language understanding, machine translation is often utilized to enhance the transferability of models across languages, either by translating the training data from the source language to the target, or from the target to the source to aid inference. However, in cross-lingual machine reading comprehension (MRC), it is difficult to perform a deep level of assistance to enhance cross-lingual transfer because of the variation of answer span positions in different languages. In this paper, we propose X-STA, a new approach for cross-lingual MRC. Specifically, we leverage an attentive teacher to subtly transfer the answer spans of the source language to the answer output space of the target. A Gradient-Disentangled Knowledge Sharing technique is proposed as an improved cross-attention block. In addition, we force the model to learn semantic alignments from multiple granularities and calibrate the model outputs with teacher guidance to enhance cross-lingual transferability. Experiments on three multi-lingual MRC datasets show the effectiveness of our method, outperforming state-of-the-art approaches.