Current Video Large Language Models (VideoLLMs) suffer from quadratic computational complexity and key-value cache scaling, due to their reliance on processing excessive redundant visual tokens. To address this problem, we propose SharpV, a minimalist and efficient method for adaptive pruning of visual tokens and KV cache. Different from most uniform compression approaches, SharpV dynamically adjusts pruning ratios based on spatial-temporal information. Remarkably, this adaptive mechanism occasionally achieves performance gains over dense models, offering a novel paradigm for adaptive pruning. During the KV cache pruning stage, based on observations of visual information degradation, SharpV prunes degraded visual features via a self-calibration manner, guided by similarity to original visual features. In this way, SharpV achieves hierarchical cache pruning from the perspective of information bottleneck, offering a new insight into VideoLLMs' information flow. Experiments on multiple public benchmarks demonstrate the superiority of SharpV. Moreover, to the best of our knowledge, SharpV is notably the first two-stage pruning framework that operates without requiring access to exposed attention scores, ensuring full compatibility with hardware acceleration techniques like Flash Attention.