Data pruning (DP), as an oft-stated strategy to alleviate heavy training burdens, reduces the volume of training samples according to a well-defined pruning method while striving for near-lossless performance. However, existing approaches, which commonly select highly informative samples, can lead to biased gradient estimation compared to full-dataset training. Furthermore, the analysis of this bias and its impact on final performance remains ambiguous. To address these challenges, we propose OrderDP, a plug-and-play framework that aims to obtain stable, unbiased, and near-lossless training acceleration with theoretical guarantees. Specifically, OrderDP first randomly selects a subset and then chooses the top-$q$ samples, where unbiasedness is established with respect to a surrogate loss. This ensures that OrderDP conducts unbiased training in terms of the surrogate objective. We further establish convergence and generalization analyses, elucidating how OrderDP affects optimal performance and enables well-controlled acceleration while ensuring guaranteed final performance. Empirically, we evaluate OrderDP against comprehensive baselines on CIFAR-10, CIFAR-100, and ImageNet-1K, demonstrating competitive accuracy, stable convergence, and exact control -- all with a simpler design and faster runtime, while reducing training cost by over 40%. Delivering both strong performance and computational efficiency, our method serves as a robust and easily adaptable tool for data-efficient learning. The code is publicly available at https://github.com/shengze-xu/OrderDP.