In order to promote green and sustainable development of the transportation industry, an increasing number of logistics companies have begun to deploy electric vehicles (EVs) to provide urban distribution services. This paper studies a Half-Open Time-Dependent Multi-Depot Electric Vehicle Routing Problem Considering Battery Recharging and Swapping (HOTDMDEVRPBRS) in last-mile delivery. Based on the calculation functions of EV energy consumption, travel time, and carbon emissions under the time-dependent road network, a mixed integer programming model is formulated. The goal of the model is to minimize the economic cost and environmental cost of logistics companies. Given the complexity of the problem, this paper designs a multi-objective simulated annealing algorithm (SAA). Finally, this paper carries out comprehensive computational experiments to verify and evaluate the performance of the proposed model and method and examines the economic and environmental benefits brought by the Half-Open Joint Distribution Mode (HOJDM). According to the results, SAA shows good performance and provides a high-quality solution. Meanwhile, the HOJDM significantly reduces the total cost and carbon emissions of logistics enterprises and provides valuable suggestions for enterprise managers and government decision-makers.