Knee osteoarthritis (OA) is one of the highest disability factors in the world in humans. This musculoskeletal disorder is assessed from clinical symptoms, and typically confirmed via radiographic assessment. This visual assessment done by a radiologist requires experience, and suffers from high inter-observer variability. The recent development in the literature has shown that deep learning (DL) methods can reliably perform the OA severity assessment according to the gold standard Kellgren-Lawrence (KL) grading system. However, these methods require large amounts of labeled data, which are costly to obtain. In this study, we propose the Semixup algorithm, a semi-supervised learning (SSL) approach to leverage unlabeled data. Semixup relies on consistency regularization using in- and out-of-manifold samples, together with interpolated consistency. On an independent test set, our method significantly outperformed other state-of-the-art SSL methods in most cases, and even achieved a comparable performance to a well-tuned fully supervised learning (SL) model that required over 12 times more labeled data.