To answer this question accurately is very difficult if you are not a scientist but often people have accidents that results in them being in a coma for an extended period, where their physical body is alive but their mind is not conscious. If the mind is not conscious at all here then that physical body is living without mind (however from a Buddhist perspective, this is probably not a "human" living since, in Buddhism, the word translated as "human" means to have a reflective & wise mind).
Also, there is a meditation state where the mind becomes unconscious, called 'the cessation of perception & feeling'. This meditative state is compared to a dead body, where even breathing cannot be felt yet the 'life force' or 'vitality' of the body & heat remain.
For example, in the Buddhist scriptures, there are stories about monks that enter into the meditation state of 'the cessation of perception & feeling' & people watch them meditating (not moving) under a tree for many days, believe they are dead & try to bury or cremate them.
Therefore, it appears it is possible to that a 'human' can live without mind.
What is the difference between one who is dead, who has completed his time; and a monk who has attained the cessation of perception & feeling?
In the case of the one who is dead, who has completed his time, his bodily fabricator (breathing)...his verbal fabricator (thinking) ... his mental fabricator (perception & feeling) have ceased & subsided, his vitality is exhausted, his heat subsided & his (five sense) faculties (eye, ears, nose, tongue & body nervous system) are scattered.
But in the case of a monk who has attained the cessation of perception & feeling, his bodily fabricator... his verbal fabricator ... his mental fabricators have ceased & subsided, his vitality is not exhausted, his heat has not subsided & his (five sense) faculties are exceptionally clear (pure).
This is the difference between one who is dead, who has completed his time, and a monk who has attained the cessation of perception & feeling.