Enterprise adoption of cloud-based AI agents faces a fundamental privacy dilemma: leveraging powerful cloud models requires sharing sensitive data, while local processing limits capability. Current agent frameworks like MCP and A2A assume complete data sharing, making them unsuitable for enterprise environments with confidential information. We present SplitAgent, a novel distributed architecture that enables privacy-preserving collaboration between enterprise-side privacy agents and cloud-side reasoning agents. Our key innovation is context-aware dynamic sanitization that adapts privacy protection based on task semantics -- contract review requires different sanitization than code review or financial analysis. SplitAgent extends existing agent protocols with differential privacy guarantees, zero-knowledge tool verification, and privacy budget management. Through comprehensive experiments on enterprise scenarios, we demonstrate that SplitAgent achieves 83.8\% task accuracy while maintaining 90.1\% privacy protection, significantly outperforming static approaches (73.2\% accuracy, 79.7\% privacy). Context-aware sanitization improves task utility by 24.1\% over static methods while reducing privacy leakage by 67\%. Our architecture provides a practical path for enterprise AI adoption without compromising sensitive data.