The pretrained large language models (LLMs) are finetuned with labeled data for better instruction following ability and alignment with human values. In this paper, we study the learning dynamics of LLM finetuning on reasoning tasks and reveal the uncovered over-memorization phenomenon during a specific stage of LLM finetuning. At this stage, the LLMs have excessively memorized training data and exhibit high test perplexity while maintaining good test accuracy. We investigate the conditions that lead to LLM over-memorization and find that training epochs and large learning rates contribute to this issue. Although models with over-memorization demonstrate comparable test accuracy to normal models, they suffer from reduced robustness, poor out-of-distribution generalization, and decreased generation diversity. Our experiments unveil the over-memorization to be broadly applicable across different tasks, models, and finetuning methods. Our research highlights that overparameterized, extensively finetuned LLMs exhibit unique learning dynamics distinct from traditional machine learning models. Based on our observations of over-memorization, we provide recommendations on checkpoint and learning rate selection during finetuning.