Radio frequency interference (RFI) mitigation is critical to the proper operation of ultra-wideband (UWB) radar systems. This paper considers RFI mitigation for a one-bit UWB radar system, with its measurements obtained via a low-cost and high-rate sampling strategy using a known threshold varying with slow-time. We first establish a data model for the RFI sources. Then we present a relaxation based algorithm to estimate the parameters of the RFI sources from the signed measurements and thresholds. Next, a sparse method is introduced to recover the desired UWB radar echoes using the estimated RFI parameters. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed method.