Drone-mounted ground penetrating radar (GPR) has the capability to investigate terrain that is inaccessible or hazardous to humans. A linear frequency-modulated (LFM) radar with the potential for GPR applications is described based on the LimeSDR Mini software defined radio (SDR). Challenges of the LimeSDR Mini radar include the SDR's lack of support for transmitter-receiver synchronization and high bleedthrough leakage. These issues are overcome through corrective software processing techniques including deconvolution of the SDR's system impulse response and digital feed-through nulling. Feed-through nulling is effective at reducing bleedthrough leakage, achieving a 26 dB reduction in power. Although high noise can confound the identification of targets with small radar cross sections in dynamic environments, the LimeSDR Mini radar is demonstrated to display a moving target across multiple ranges. This research demonstrates the increasing accessibility of SDR radar for drone applications, as the LimeSDR Mini is lightweight and low-cost compared to high-end SDRs typically used in SDR radar.