Trustees delayed approving building plans for the proposed three-story, 140,000-square-foot structure that will sit adjacent to San Pedro Creek Park.
The school will open in 2019 with a freshman class and grow with an additional class each year, topping out at an estimated 600 students.
Alexander Acosta told reporters that "demand-driven education" is ideal, where schools listen to businesses to meet future workforce needs.
The new school, located just east of downtown, is based on the model of SAISD's successful Young Women's Leadership Academy.
Community members and parents peppered Superintendent Pedro Martinez with questions Wednesday at the third and final public meeting Fox Tech High School.
Military school districts serve populations with lower levels of poverty, which some have said make it easier for the districts to achieve at high levels.
Ultimately, the district plans to open a different school at Rodriguez Elementary's same location in the 2020-21 school year.
With 22 offerings, SAISD is home to the highest number of in-district charter schools among the state's roughly 1,200 school districts.
Plans for the central office are still tentative, but the new facility likely will be located on the site of the football field at Fox Tech.
Charter schools are merely the latest attempt by private corporations to rebrand the school reform movement and exploit public funding for profit.