The goal of spatially explainable artificial intelligence (AI) classification approach is to build a classifier to distinguish two classes (e.g., responder, non-responder) based on the their spatial arrangements (e.g., spatial interactions between different point categories) given multi-category point data from two classes. This problem is important for generating hypotheses towards discovering new immunotherapies for cancer treatment as well as for other applications in biomedical research and microbial ecology. This problem is challenging due to an exponential number of category subsets which may vary in the strength of their spatial interactions. Most prior efforts on using human selected spatial association measures may not be sufficient for capturing the relevant spatial interactions (e.g., surrounded by) which may be of biological significance. In addition, the related deep neural networks are limited to category pairs and do not explore larger subsets of point categories. To overcome these limitations, we propose a Spatial-interaction Aware Multi-Category deep neural Network (SAMCNet) architecture and contribute novel local reference frame characterization and point pair prioritization layers for spatially explainable classification. Experimental results on multiple cancer datasets (e.g., MxIF) show that the proposed architecture provides higher prediction accuracy over baseline methods. A real-world case study demonstrates that the proposed work discovers patterns that are missed by the existing methods and has the potential to inspire new scientific discoveries.