Training-free video understanding methods leverage the strong image comprehension capabilities of pre-trained vision language models (VLMs) by treating videos as a sequences of static frames, thus obviating the need for costly video-specific training. However, this paradigm often suffers from severe visual redundancy and high computational overhead, especially when processing long videos. Crucially, existing keyframe selection strategies, especially those based on CLIP similarity, are prone to biases and may inadvertently overlook critical frames, resulting in suboptimal video comprehension. To address these significant challenges, we propose KTV, a novel two-stage framework for efficient and effective training-free video understanding. In the first stage, KTV performs question-agnostic keyframe selection by clustering frame-level visual features, yielding a compact, diverse, and representative subset of frames that mitigates temporal redundancy. In the second stage, KTV applies key visual token selection, pruning redundant or less informative tokens from each selected keyframe based on token importance and redundancy, which significantly reduces the number of tokens fed into the LLM. Extensive experiments on the Multiple-Choice VideoQA task demonstrate that KTV outperforms state-of-the-art training-free baselines while using significantly fewer visual tokens, e.g., only 504 tokens for a 60 min video with 10800 frames, achieving 44.8\% accuracy on the MLVU-Test benchmark. In particular, KTV also exceeds several training-based approaches on certain benchmarks. The code is released anonymously in the supplementary materials.