While Large Vision-Language Models (LVLMs) demonstrate exceptional multi-modal capabilities, the quadratic computational cost of processing high-resolution visual tokens remains a critical bottleneck. Though recent token reduction strategies attempt to accelerate inference, such methods inadequately exploit attention values and fail to address token redundancy. More critically, they overlook the ``attention shift'' phenomenon inherent in LVLMs, which skews token attention scores. In this work, we propose ASAP, a novel training-free, KV-Cache-compatible pruning recipe that comprehensively addresses these limitations. First, we mitigate the attention shift by utilizing a dynamic bidirectional soft attention mask, ensuring the selection of genuinely informative tokens rather than naive attention-based selection. Second, we posit that high semantic redundancy within the token set degrades performance. We therefore introduce a weighted soft merging component that merges semantically similar tokens, preserving only the most feature-dense visual patches for subsequent layers. ASAP achieves virtually lossless compression of visual context, retaining 99.02% of the original LLaVA-NeXT-7B performance while aggressively slashing computational FLOPs by ~80%.