Recent advancements in deep learning have greatly enhanced 3D object recognition, but most models are limited to closed-set scenarios, unable to handle unknown samples in real-world applications. Open-set recognition (OSR) addresses this limitation by enabling models to both classify known classes and identify novel classes. However, current OSR methods rely on global features to differentiate known and unknown classes, treating the entire object uniformly and overlooking the varying semantic importance of its different parts. To address this gap, we propose Salience-Aware Structured Separation (SASep), which includes (i) a tunable semantic decomposition (TSD) module to semantically decompose objects into important and unimportant parts, (ii) a geometric synthesis strategy (GSS) to generate pseudo-unknown objects by combining these unimportant parts, and (iii) a synth-aided margin separation (SMS) module to enhance feature-level separation by expanding the feature distributions between classes. Together, these components improve both geometric and feature representations, enhancing the model's ability to effectively distinguish known and unknown classes. Experimental results show that SASep achieves superior performance in 3D OSR, outperforming existing state-of-the-art methods.