Currently, the use of biosensor-enabled mobile healthcare workflow applications in mobile edge-cloud-enabled systems is increasing progressively. These applications are heavyweight and divided between a thin client mobile device and a thick server edge cloud for execution. Application partitioning is a mechanism in which applications are divided based on resource and energy parameters. However, existing application-partitioning schemes widely ignore security aspects for healthcare applications. This study devises a dynamic application-partitioning workload task-scheduling-secure (DAPWTS) algorithm framework that consists of different schemes, such as min-cut algorithm, searching node, energy-enabled scheduling, failure scheduling, and security schemes. The goal is to minimize the energy consumption of nodes and divide the application between local nodes and edge nodes by applying the secure min-cut algorithm. Furthermore, the study devises the secure-min-cut algorithm, which aims to migrate data between nodes in a secure form during application partitioning in the system. After partitioning the applications, the node-search algorithm searches optimally to run applications under their deadlines. The energy and failure schemes maintain the energy consumption of the nodes and the failure of the system. Simulation results show that DAPWTS outperforms existing baseline approaches by 30% in terms of energy consumption, deadline, and failure of applications in the system.