Large vision-language models (LVLMs) achieve strong performance on image and video understanding tasks, but their inference efficiency is constrained by the large number of visual tokens produced by vision encoders. Most existing visual token compression methods estimate token importance from attention scores or representation properties at specific layers, overlooking how visual tokens evolve across the vision encoder. Such layer-specific criteria may provide incomplete importance estimates and limit performance preservation after compression. To address this issue, we analyze layer-wise visual token evolution directions and observe that tokens form multiple group evolution directions across vision-encoder layers. Our analysis further shows that informative tokens tend to exhibit persistent deviations from common group evolution directions. Based on this observation, we propose EvoCut, a training-free and attention-free visual token compression method that estimates token importance from multi-layer evolution deviation. Experimental results show that EvoCut can retain only 11.1\% of the visual tokens on LLaVA-1.5-7B while preserving 94.4\% of the average performance, demonstrating its effectiveness in balancing efficiency and accuracy.