Clinical named entity recognition (NER) aims to retrieve important entities within clinical narratives. Recent works have demonstrated that large language models (LLMs) can achieve strong performance in this task. While previous works focus on proprietary LLMs, we investigate how open NER LLMs, trained specifically for entity recognition, perform in clinical NER. Our initial experiment reveals significant contrast in performance for some clinical entities and how a simple exploitment on entity types can alleviate this issue. In this paper, we introduce a novel framework, entity decomposition with filtering, or EDF. Our key idea is to decompose the entity recognition task into several retrievals of entity sub-types and then filter them. Our experimental results demonstrate the efficacies of our framework and the improvements across all metrics, models, datasets, and entity types. Our analysis also reveals substantial improvement in recognizing previously missed entities using entity decomposition. We further provide a comprehensive evaluation of our framework and an in-depth error analysis to pave future works.