Dataset pruning aims to construct a coreset capable of achieving performance comparable to the original, full dataset. Most existing dataset pruning methods rely on snapshot-based criteria to identify representative samples, often resulting in poor generalization across various pruning and cross-architecture scenarios. Recent studies have addressed this issue by expanding the scope of training dynamics considered, including factors such as forgetting event and probability change, typically using an averaging approach. However, these works struggle to integrate a broader range of training dynamics without overlooking well-generalized samples, which may not be sufficiently highlighted in an averaging manner. In this study, we propose a novel dataset pruning method termed as Temporal Dual-Depth Scoring (TDDS), to tackle this problem. TDDS utilizes a dual-depth strategy to achieve a balance between incorporating extensive training dynamics and identifying representative samples for dataset pruning. In the first depth, we estimate the series of each sample's individual contributions spanning the training progress, ensuring comprehensive integration of training dynamics. In the second depth, we focus on the variability of the sample-wise contributions identified in the first depth to highlight well-generalized samples. Extensive experiments conducted on CIFAR and ImageNet datasets verify the superiority of TDDS over previous SOTA methods. Specifically on CIFAR-100, our method achieves 54.51% accuracy with only 10% training data, surpassing random selection by 7.83% and other comparison methods by at least 12.69%. Our codes are available at https://github.com/zhangxin-xd/Dataset-Pruning-TDDS.