Live streaming has emerged as one of the fastest-growing forms of online media, enabling instant content broadcasting and real-time engagement between users and streamers. Despite the effectiveness of existing recommendation algorithms in this domain, they often suffer from limited utilization of computational resources, with low FLOPs that hinder further performance enhancement. Generative recommendation techniques, which have gained traction in various industrial tasks, offer a promising avenue for improving live streaming recommendations. However, directly applying generative methods to live streaming is non-trivial due to two major challenges: (1) static semantic IDs (SIDs) cannot reflect the rapidly changing nature of live room content; and (2) generative pipelines generally do not incorporate user--streamer interaction signals (e.g., likes, orders), which are critical for modeling user intent toward both the streamer and showcased products. To address these challenges, we introduce SSRLive: Dynamic Semantic ID-guided Streaming Recommendation for Live platforms. The proposed framework integrates a generative module and a discriminative module in a unified architecture. The generative component employs an encoder-decoder design to produce both static and dynamic SIDs, enabling timely representation of live room content while leveraging multimodal information. The discriminative component refines task-specific representations by combining SIDs with user features, augments them with user-streamer interaction data, and performs multi-task predictions. Online A/B tests in real-world deployment demonstrate tangible benefits: watch time (+3.38%), GMV (+0.72%), follower growth (+3.12%), and interaction volume (+2.92%). These improvements highlight the effectiveness and business value of SSRLive, which is now fully deployed, serving hundreds of millions of active users.