Physical immortality is something different from immortality of our true self, our evolving soul, our psychic being, which is the unending existence of our being through multiple births. Physical immortality is where we are able to live as long as we choose in the physical body. This will be possible when the cellular essence of our being is responsive to the descending or evoked Spiritual Force, and therefore the body's programming will change so that there will no longer be illness, decay, and death.
The Mother worked on this transformational issue for much of Her life, enabling the cells of Her body to be responsive to the incoming supramental power, forging a path for us to follow. She indicated that Sri Aurobindo or perhaps someone else would return with a New Body that is supramentalized with the capacity of willed physical immortality. That New Person would have centers of consciousness instead of the current organs, digestive systems, fluid and breath circulation, et al. She described this being as tall, svelte, sexless, emanating light, which would be an evolutionary change into a new-type of human species.
Mother had many visions and personal experiences in this area. For example, once She saw Her own body become the supramental being at the subtle plane. She actually, physically saw it. Dozens of these sorts of experiences of Hers are described in great detail by Her in Her 4000 page diary called Agenda.