A diaphragm wall is used in a deep foundation pit project in Nanjing that crosses a soft high-level pressurized water-sand interlayer. This weak interlayer is recognized as prone to local instability during trenching, which can result in collapse or shrinkage and compromise construction safety. To investigate the local instability mechanism of the diaphragm wall during trenching, a three-dimensional computational model was established by considering soil arch effects. The local stability safety factor of the trench wall was computed. Ultrasonic monitoring and on-site trenching tests were carried out to validate the calculation results. The results show that this three-dimensional model effectively evaluates the local stability of the trench wall at the weak interlayer. The soil arch height behind the trench wall is positively correlated with trench length and soil friction angle. Increasing the mud density and raising the mud level improves the local stability safety factor. An optimized mud ratio satisfies both economic and safety requirements, and raises the overall stability coefficient and the local stability coefficient of the trench wall to 1.5 and 1.25, respectively. The research findings provide a reference for designing stable and economical diaphragm wall trenching in similar engineering projects.