The growing memory footprint of the Key-Value (KV) cache poses a severe scalability bottleneck for long-context Large Language Model (LLM) inference. While KV cache eviction has emerged as an effective solution by discarding less critical tokens, existing token-, block-, and sentence-level compression methods struggle to balance semantic coherence and memory efficiency. To this end, we introduce SABlock, a \underline{s}emantic-aware KV cache eviction framework with \underline{a}daptive \underline{block} sizes. Specifically, SABlock first performs semantic segmentation to align compression boundaries with linguistic structures, then applies segment-guided token scoring to refine token importance estimation. Finally, for each segment, a budget-driven search strategy adaptively determines the optimal block size that preserves semantic integrity while improving compression efficiency under a given cache budget. Extensive experiments on long-context benchmarks demonstrate that SABlock consistently outperforms state-of-the-art baselines under the same memory budgets. For instance, on Needle-in-a-Haystack (NIAH), SABlock achieves 99.9% retrieval accuracy with only 96 KV entries, nearly matching the performance of the full-cache baseline that retains up to 8K entries. Under a fixed cache budget of 1,024, SABlock further reduces peak memory usage by 46.28% and achieves up to 9.5x faster decoding on a 128K context length.