Split learning of deep neural networks (SplitNN) has provided a promising solution to learning jointly for the mutual interest of a guest and a host, which may come from different backgrounds, holding features partitioned vertically. However, SplitNN creates a new attack surface for the adversarial participant, holding back its practical use in the real world. By investigating the adversarial effects of highly threatening attacks, including property inference, data reconstruction, and feature hijacking attacks, we identify the underlying vulnerability of SplitNN and propose a countermeasure. To prevent potential threats and ensure the learning guarantees of SplitNN, we design a privacy-preserving tunnel for information exchange between the guest and the host. The intuition is to perturb the propagation of knowledge in each direction with a controllable unified solution. To this end, we propose a new activation function named R3eLU, transferring private smashed data and partial loss into randomized responses in forward and backward propagations, respectively. We give the first attempt to secure split learning against three threatening attacks and present a fine-grained privacy budget allocation scheme. The analysis proves that our privacy-preserving SplitNN solution provides a tight privacy budget, while the experimental results show that our solution performs better than existing solutions in most cases and achieves a good tradeoff between defense and model usability.