Unsupervised rationale extraction aims to extract text snippets to support model predictions without explicit rationale annotation. Researchers have made many efforts to solve this task. Previous works often encode each aspect independently, which may limit their ability to capture meaningful internal correlations between aspects. While there has been significant work on mitigating spurious correlations, our approach focuses on leveraging the beneficial internal correlations to improve multi-aspect rationale extraction. In this paper, we propose a Multi-Aspect Rationale Extractor (MARE) to explain and predict multiple aspects simultaneously. Concretely, we propose a Multi-Aspect Multi-Head Attention (MAMHA) mechanism based on hard deletion to encode multiple text chunks simultaneously. Furthermore, multiple special tokens are prepended in front of the text with each corresponding to one certain aspect. Finally, multi-task training is deployed to reduce the training overhead. Experimental results on two unsupervised rationale extraction benchmarks show that MARE achieves state-of-the-art performance. Ablation studies further demonstrate the effectiveness of our method. Our codes have been available at https://github.com/CSU-NLP-Group/MARE.