Radio frequency interference (RFI) mitigation is critical to the proper operation of ultrawideband (UWB) radar systems because RFI can severely degrade the radar imaging capability and target detection performance. In this article, we address the RFI mitigation problem for one-bit UWB radar systems. A one-bit UWB system obtains its signed measurements via a low-cost and high rate sampling scheme, referred to as the continuous time binary value (CTBV) technology. This sampling strategy compares the signal to a known threshold that varies with slow-time and can be used to achieve a high sampling rate and quantization resolution with simple and affordable hardware. This article establishes a proper data model for the RFI sources and proposes a novel RFI mitigation method for the one-bit UWB radar system that uses the CTBV sampling technique. Specifically, we model the RFI sources as a sum of sinusoids with frequencies fixed during the coherent processing interval (CPI) and we exploit the sparsity of the RFI spectrum. We use an extended majorization-minimization-based 1bRELAX algorithm, referred to as 1bMMRELAX, to estimate the RFI source parameters from the signed measurements obtained by using the CTBV sampling strategy. We also devise a new fast frequency initialization method for the extended 1bMMRELAX algorithm to improve its computational efficiency. Moreover, a sparse method is introduced to recover the desired radar echoes using the estimated RFI parameters. Both simulated and experimental results are presented to demonstrate that our proposed algorithm outperforms the existing digital integration method, especially for severe RFI cases.