The recent decade has witnessed an upsurge in the demands of intelligent and simplified Internet of Things (IoT) networks that provide ultra-low-power communication for numerous miniaturized devices. Although the research community has paid great attention to wireless protocol designs for these networks, researchers are handicapped by the lack of an energy-efficient software-defined radio (SDR) platform for fast implementation and experimental evaluation. Current SDRs perform well in battery-equipped systems, but fail to support miniaturized IoT devices with stringent hardware and power constraints. This paper takes the first step toward designing an ultra-low-power SDR that satisfies the ultra-low-power or even battery-free requirements of intelligent and simplified IoT networks. To achieve this goal, the core technique is the effective integration of µW-level backscatter in our SDR to sidestep power-hungry active radio frequency chains. We carefully develop a novel circuit design for efficient energy harvesting and power control, and devise a competent solution for eliminating the harmonic and mirror frequencies caused by backscatter hardware. We evaluate the proposed SDR using different modulation schemes, and it achieves a high data rate of 100 kb/s with power consumption less than 200 µW in the active mode and as low as 10 µW in the sleep mode. We also conduct a case study of railway inspection using our platform, achieving 1 kb/s battery-free data delivery to the monitoring unmanned aerial vehicle at a distance of 50 m in a real-world environment, and provide two case studies on smart factories and logistic distribution to explore the application of our platform.