Thanks to the promising wireless power transmission (WPT) technology, wireless-powered Internet of Things (WPIoT) can significantly improve the sustainable service ability of Internet of Things (IoT) with low personnel maintenance costs, and thus, shows remarkable and broad prospects in many applications, especially under the abominable and dangerous environment. Minimum delay data aggregation scheduling (MAS) is a problem of cardinal significance in WPIoT with the objective of timely collecting the data of IoT devices. However, due to the residual energy limitation of IoT devices, WPIoT shows the special feature of adopting the store-charge-and-forward communication mode, which brings new research challenges on designing efficient solutions to the MAS problem. We show that the MAS problem under the physical interference model in WPIoT is NP-hard. To tackle this problem, we propose a delay-efficient data aggregation scheduling algorithm called HADA based on an active data aggregation tree construction method and a novel hypergraph-based link scheduling method. Extensive numerical experiments are conducted to evaluate the performance of our proposed algorithm. The results demonstrate that our HADA algorithm can efficiently improve the performance compared with the existing baseline algorithms.