User purchase decisions are driven by complex, multi-faceted intentions that evolve across different temporal horizons (e.g., immediate needs, transitional interests, and long-term preferences). However, existing sequential methods often treat user sequences as unified blocks, overlooking the dynamic evolution of user intents at different granularities, while also lacking robustness against prevalent noise in real-world interaction data. This paper proposes Multi-granularity Intent Modeling with Adversarial Robustness for Sequential Recommendation (MIMAR-SRec), a framework that models latent user intentions at multiple granularities. Specifically, MIMAR-SRec integrates multi-granularity intent representation across different contextual windows to capture evolving user interests, dual-perspective contrastive learning that aligns user representations with both intent prototypes and cross-user sequences, and intent-similarity adversarial robustness that systematically enhances model stability against interaction, temporal, and preference noise through controlled perturbations. By integrating multi-granularity intent modeling with adversarial training, MIMAR-SRec enables simultaneous fine-grained underlying intent modeling and noise-resistant recommendations. Extensive experiments on four widely used benchmark datasets demonstrate that MIMAR-SRec outperforms state-of-the-art baselines, particularly in long-tail item recommendation and noisy interaction scenarios. Our code is available in the appendix and will be open-sourced upon paper acceptance.