This article seeks for a distributed learning solution for the visual transformer (ViT) architectures. Compared to convolutional neural network (CNN) architectures, ViTs often have larger model sizes, and are computationally expensive, making federated learning (FL) ill-suited. Split learning (SL) can detour this problem by splitting a model and communicating the hidden representations at the split-layer, also known as smashed data. Notwithstanding, the smashed data of ViT are as large as and as similar as the input data, negating the communication efficiency of SL while violating data privacy. To resolve these issues, we propose a new form of CutSmashed data by randomly punching and compressing the original smashed data. Leveraging this, we develop a novel SL framework for ViT, coined CutMixSL, communicating CutSmashed data. CutMixSL not only reduces communication costs and privacy leakage, but also inherently involves the CutMix data augmentation, improving accuracy and scalability. Simulations corroborate that CutMixSL outperforms baselines such as parallelized SL and SplitFed that integrates FL with SL.