Accurate identification of Kirsten Ras (KRAS) gene mutation status is essential to avoid ineffective medication in colorectal cancer patients. In the field of computer-aided diagnosis, Mamba-based visual models have recently attracted much attention for their superior remote modeling and linear efficiency. However, most existing methods focus on natural images and often overlook the importance of maintaining spatial locality relationships between adjacent pixels when converting non-causal visual images into ordered block sequences. In this paper, we build a Segmentation-based Spatial Continuity Intensifying State Space Model (SSCI-SSM) to identify KRAS mutation status in colorectal cancer patients from T2-weighted MRI. Specifically, a Mamba variant is designed for medical images with spatial continuity processing capabilities, while integrating a state-space model with the Hilbert scanning technique to construct a Continuity-Intensifying State Space Block (CISSB). Additionally, we correlate and unify global and local patterns to construct a Feature Fusion Enhancement Module (FFEM) for comprehensive image feature modeling. The model combines segmentation and classification tasks, explores multi-scale features during segmentation, captures discriminative features, and achieves customized and efficient modeling representations. The experimental results demonstrate that our proposed SSCI-SSM achieves an accuracy of 91.48%, with an AUC value of 97.08, which is at least 4.34% improvement than the state-of-the-art methods. Notably, it requires only a floating-point computation volume of 6.97G, realizing minimal computational complexity and number of parameters while maintaining high performance. In clinical practice, especially in resource-constrained environments, our proposed method can provide physicians with real-time and efficient auxiliary support for diagnosing KRAS gene mutation status.