Traditional data processing pipelines are typically static and handcrafted for specific tasks, limiting their adaptability to evolving requirements. While general-purpose agents and coding assistants can generate code for well-understood data pipelines, they lack the ability to autonomously monitor, manage, and optimize an end-to-end pipeline once deployed. We present \textbf{Autonomous Data Processing using Meta-agents} (ADP-MA), a framework that dynamically constructs, executes, and iteratively refines data processing pipelines through hierarchical agent orchestration. At its core, \textit{meta-agents} analyze input data and task specifications to design a multi-phase plan, instantiate specialized \textit{ground-level agents}, and continuously evaluate pipeline performance. The architecture comprises three key components: a planning module for strategy generation, an orchestration layer for agent coordination and tool integration, and a monitoring loop for iterative evaluation and backtracking. Unlike conventional approaches, ADP-MA emphasizes context-aware optimization, adaptive workload partitioning, and progressive sampling for scalability. Additionally, the framework leverages a diverse set of external tools and can reuse previously designed agents, reducing redundancy and accelerating pipeline construction. We demonstrate ADP-MA through an interactive demo that showcases pipeline construction, execution monitoring, and adaptive refinement across representative data processing tasks.