Future space ventures will likely require exploitation of near-Earth asteroid resources. Moreover, it can be envisaged that asteroids may host habitats in their interiors. In fact, a cavern inside an asteroid would be a natural radiation shield against cosmic radiation and may also serve as a confined environment for storage of mined material such as water ice or other processed volatiles such as propellants. To this end, this paper proposes to leverage the asteroid rotational self-energy to remove material from the asteroid interiors and create a spherical cavern, by means of the orbital siphon concept. The siphon is a chain of tether-connected payload masses (the asteroid material), which exploits the rotation of the asteroid for the delivery of mass from the asteroid to escape. Under certain conditions the siphon can be initiated to ensure self-sustained flow of mass from the asteroid to escape. A net orbital siphon effect is generated by connecting new payloads at the bottom of the chain while releasing the upper payloads. Key parameters are discussed, such as the required siphon dimension and the maximum size of the internal cavity that can be excavated, as a function of the asteroid rotational period. Moreover, assuming elastic material behaviour, a closed-form expression for the stress tensor is found and a failure criterion is used to identify regions in the asteroid interiors subjected to the larger stresses. It is shown that the conditions for failure are relaxed as the radius of the internal void increases.