The proliferation of deep learning (DL) has led to the emergence of privacy and security concerns. To address these issues, secure Two-party computation (2PC) has been proposed as a means of enabling privacy-preserving DL computation. However, in practice, 2PC methods often incur high computation and communication overhead, which can impede their use in large-scale systems. To address this challenge, we introduce RRNet, a systematic framework that aims to jointly reduce the overhead of MPC comparison protocols and accelerate computation through hardware acceleration. Our approach integrates the hardware latency of cryptographic building blocks into the DNN loss function, resulting in improved energy efficiency, accuracy, and security guarantees. Furthermore, we propose a cryptographic hardware scheduler and corresponding performance model for Field Programmable Gate Arrays (FPGAs) to further enhance the efficiency of our framework. Experiments show RRNet achieved a much higher ReLU reduction performance than all SOTA works on CIFAR-10 dataset.