Semantic top-𝐾 selection with cross-encoder rerankers underpins of on-device AI services, such as retrieval-augmented generation, agent memory, and personalized recommendation. However, its latency and memory demands dominate end-to-end budgets on edge hardware. Revisiting the objective of top-𝐾 selection, we reveal that only relative rankings matter, not exact per-candidate scores. We further observe sequence-level sparsity: relative rankings stabilize early in intermediate layers, allowing pruning opportunities prior to completing full inference. Building on this insight, we propose monolithic forwarding and develop a training-free inference system, PRISM. By maintaining a global view of all candidates, it reduces latency through progressive cluster pruning. It also bounds peak memory usage by strategically overlapping I/O with computation via dual-layer sliding window and chunked execution. We evaluate PRISM against state-of-the-art baselines on rerankers from 0.6 B to 8 B parameters across Apple M2 and RTX 5070. PRISM consistently reduces latency by up to 89.0% and peak memory by up to 94.9% in microbenchmarks, without any loss in precision. Across three real-world on-device AI applications, PRISM lowers latency by 11.6%–51.0% and peak memory by 18.6%–77.8%, demonstrating substantial improvements in efficiency and deployability.