Video Temporal Grounding (VTG) localizes the temporal boundaries of a query-relevant moment in long, untrimmed videos, making video-language-model (VLM) pipelines prohibitively expensive. While recent training-free visual token pruning has shown success in video question answering, naively applying these objectives to VTG often causes drastic degradation, as VTG crucially depends on boundary-sensitive evidence and cross-frame reasoning chains. We therefore identify two VTG-specific pruning principles: Evidence Retention (ER), which keeps query-critical patches especially around event boundaries, and Connectivity Strength (CS), which preserves token-level cross-frame connectivity for long-range evidence aggregation. Building on these insights, we propose SemVID, a training-free pruning framework that constructs a compact yet coherent token subset with complementary semantic roles. SemVID first allocates per-frame token budgets by balancing query relevance and inter-frame variation to avoid over-pruned segments, and then selects three types of tokens: object tokens for diverse query-critical evidence, motion tokens to capture meaningful transitions and serve as cross-frame relays, and a small set of context tokens for scene continuity. Extensive experiments on VTG benchmarks show that SemVID achieves a strong accuracy-efficiency trade-off, retaining up to 95.4% mIoU with only 12.5% visual tokens and delivering up to a 5.8x prefill speedup, consistently outperforming prior methods under the same budgets.