A manufacturing method for a metal part uses a tooling assembly. The tooling assembly includes a counter-form and a deformable core which includes inner and outer skins, a honeycomb structure positioned between the inner and outer skins, and a brazing material interposed between the honeycomb structure and the inner and outer skins. In particular, the core is closed by a lid equipped with ducts through which a gas is introduced. The manufacturing method includes the following steps: positioning the tooling assembly in a vacuum furnace; introducing a pressurized gas directly inside an inner skin of the core of the tooling assembly; purging the pressurized gas from an inner portion of the inner skin of the tooling assembly; and dismounting the tooling assembly so as to extract a metal part manufactured.