As the portable consumer healthcare devices become increasingly prevalent, ubiquitously accessible healthcare support has been crucial for the advancement of healthcare systems. However, these portable consumer devices often lack the capacity to support complex healthcare AI services. With the advancement of mobile edge computing, split learning (SL) emerges as a promising solution by offloading portions of model training to auxiliary servers, thereby reducing computational load on consumer devices. Nevertheless, the frequent transmission of intermediate data in mobile edge networks increases communication energy consumption and privacy risks. To tackle these challenges, we propose the Clipping Quantized Split Learning (CQSL) scheme. Unlike conventional methods, CQSL integrates quantization with mutual information constraints to balance privacy, energy efficiency, and accuracy, with proven convergence. Simulations demonstrate that CQSL excels in privacy preservation, energy reduction, and model accuracy retention, presenting a secure and efficient AI solution for healthcare edge devices.