Background: Triple-negative breast cancer (TNBC) remains the most aggressive and lethal subtype of breast cancer, characterized by the lack of estrogen receptor, progesterone receptor, and HER2 amplification. Neoadjuvant chemotherapy (NAC) is the standard of care; however, approximately 60-70% of patients fail to achieve a pathological complete response (pCR), leading to early relapse and poor overall survival. The biological heterogeneity of TNBC, driven by complex genomic instability and tumor microenvironment (TME) interactions, hampers the efficacy of traditional clinical prognostication. Methods: We developed "MultiResist-Net," a novel multimodal deep learning framework that integrates transcriptional profiles (RNA-seq), somatic mutation landscapes, and clinical-demographic variables to predict pCR status in TNBC patients. We harmonized data from The Cancer Genome Atlas (TCGA-BRCA, n=158) and the METABRIC cohort (n=212) for training and internal validation, with further external testing on the I-SPY 2 TRIAL cohort (n=140). Our architecture utilizes a Graph Neural Network (GNN) to model protein-protein interaction (PPI) networks from transcriptomic data, coupled with a cross-attention mechanism to fuse clinical and genomic embeddings. Results: MultiResist-Net achieved an Area Under the Receiver Operating Characteristic Curve (AUROC) of 0.88 (95% CI: 0.85-0.91) and an F1-score of 0.84 in the hold-out test set, significantly outperforming unimodal baselines (RNA-only AUROC 0.76) and traditional machine learning models (XGBoost AUROC 0.81). Biological interpretation utilizing integrated gradients revealed key predictive features, including the upregulation of drug efflux transporters (ABCB1, ABCC1) and stemness markers (ALDH1A1, SOX2), as well as a distinct immune-excluded TME signature characterized by low CD8A expression and high TGF-beta signaling. Kaplan-Meier analysis demonstrated that patients predicted as "high-risk" by our model had significantly shorter recurrence-free survival (HR = 3.45, p < 0.001). Conclusion: Multimodal AI integration significantly enhances the prediction of chemotherapy response in TNBC compared to single-omics or clinical features alone. This study provides a clinically translatable tool for early stratification of high-risk TNBC patients, potentially guiding the escalation to novel targeted therapies or immunotherapy in non-responders.