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Recently, vision transformer (ViT) has started to outpace the conventional CNN in computer vision tasks. Considering privacy-preserving distributed learning with ViT, federated learning (FL) communicates models, which becomes ill-suited due to ViT' s large model size and computing costs. Split learning (SL) detours this by communicating smashed data at a cut-layer, yet suffers from data privacy leakage and large communication costs caused by high similarity between ViT' s smashed data and input data. Motivated by this problem, we propose DP-CutMixSL, a differentially private (DP) SL framework by developing DP patch-level randomized CutMix (DP-CutMix), a novel privacy-preserving inter-client interpolation scheme that replaces randomly selected patches in smashed data. By experiment, we show that DP-CutMixSL not only boosts privacy guarantees and communication efficiency, but also achieves higher accuracy than its Vanilla SL counterpart. Theoretically, we analyze that DP-CutMix amplifies R\'enyi DP (RDP), which is upper-bounded by its Vanilla Mixup counterpart.