This article addresses the interference suppression problem in frequency-modulated continuous-wave radars. We propose an unsupervised learning framework based on an autoencoder architecture, which comprises two key modules: a unitary approximate message passing (UAMP)-based interference suppression module as the encoder and a vision transformer (ViT) reconstruction module as the decoder. For the interference suppression module, we propose a deep network by unrolling the UAMP for a sparse Bayesian learning algorithm to estimate the target signal, which exhibits sparsity in the frequency domain. The estimated target and interference components are subsequently fed into a ViT, which processes the input in patchwise fashion to capture global contextual dependencies for signal reconstruction, facilitating unsupervised learning without reliance on labeled data. To guide network training, we design a weighted loss function that combines mean-square error, sparsity control, and energy preservation, ensuring the retention of target power and sparsity while effectively suppressing interference. Both simulation and experimental results demonstrate the superior performance of the proposed network compared to state-of-the-art interference suppression approaches.