Recent advances in robust semi-supervised learning (SSL) typical filters out-of-distribution (OOD) information at the sample level. We argue that an overlooked problem of robust SSL is its corrupted information on semantic level, practically limiting the development of the field. In this paper, we take an initiative step to explore and propose a unified framework termed as OOD Semantic Pruning (OSP), aims at pruning OOD semantics out from the in-distribution (ID) features. Specifically, (i) we propose an aliasing OOD matching module to pair each ID sample with an OOD sample with semantic overlap. (ii) We design a soft orthogonality regularization, which first transforms each ID feature by suppressing its semantic component that is collinear with paired OOD sample. It then forces the predictions before and after soft orthogonality transformation to be consistent. Being practically simple, our method shows a strong performance in OOD detection and ID classification on challenging benchmarks. In particular, OSP surpasses the previous state-of-the-art by 13.7% on accuracy for ID classification and 5.9% on AUROC for OOD detection on TinyImageNet dataset. Codes are available in the supplementary material.