Low-resource target-language generation is often limited by scarce parallel data, while high-resource source-language monolingual data is abundant but difficult to use with standard supervised fine-tuning. We propose Source-Grounded Semantic Reinforcement Learning (SG-SRL), a resource-utilization framework that converts source-language monolingual data into cross-lingual semantic supervision for target-language generation. SG-SRL performs reference-free reinforcement learning (RL) on source-language data using a cross-lingual semantic reward model, instantiated by a cross-lingual reranker that scores the semantic relevance between the source input and the target-language generation. While this induces severe verbosity-based reward hacking, a lightweight recovery stage using a small parallel corpus restores fluency, conciseness, and task format while preserving the semantic gains. Experiments on Chinese-to-Thai generation show that SG-SRL improves semantic grounding and factual coverage over cold-start SFT. Additional analyses on long-form transfer and Tibetan embedding-based rewards clarify the generalization behavior of SG-SRL and show that an encoder-based semantic reward can substitute for an LLM-based reranker in a realistic low-resource language setting.