Large Language Models (LLMs) can be fine-tuned on domain-specific data to enhance their performance in specialized fields. However, such data often contains numerous low-quality samples, necessitating effective data processing (DP). In practice, DP strategies are typically developed through iterative manual analysis and trial-and-error adjustment. These processes inevitably incur high labor costs and may lead to privacy issues in high-privacy domains like healthcare due to direct human access to sensitive data. Thus, achieving automated data processing without exposing the raw data has become a critical challenge. To address this challenge, we propose LLM-AutoDP, a novel framework that leverages LLMs as agents to automatically generate and optimize data processing strategies. Our method generates multiple candidate strategies and iteratively refines them using feedback signals and comparative evaluations. This iterative in-context learning mechanism enables the agent to converge toward high-quality processing pipelines without requiring direct human intervention or access to the underlying data. To further accelerate strategy search, we introduce three key techniques: Distribution Preserving Sampling, which reduces data volume while maintaining distributional integrity; Processing Target Selection, which uses a binary classifier to identify low-quality samples for focused processing; Cache-and-Reuse Mechanism}, which minimizes redundant computations by reusing prior processing results. Results show that models trained on data processed by our framework achieve over 80% win rates against models trained on unprocessed data. Compared to AutoML baselines based on LLM agents, LLM-AutoDP achieves approximately a 65% win rate. Moreover, our acceleration techniques reduce the total searching time by up to 10 times, demonstrating both effectiveness and efficiency.