What it really means?
Destruction of the mind does not mean annihilation of the Self. The Vedantins divide the mind into the higher and the lower, of which the lower one leading to desires is asked to be destroyed.
Destruction of desires, annihilation of Ego, destruction of thoughts, all mean control of mind or annihilation of mind. Destruction of egoism, Like-Dislike (attraction and repulsion for objects) and all subtle desires alone is annihilation of mind. Annihilation of mind comes through the destruction of the subtle desires. It does not mean that you should take a sword and cut the mind to pieces.
Annihilation of mind means the death of the present form of the mind (i.e., the instinctive mind of emotions and passions), the form which perceives differences where none exists, which identifies the Self with the body. Its death really means its transformation into and, therefore, the birth of cosmic consciousness.
Vast majority of persons live in Annamaya Kosha (sheath of food or physical body) only. Their thoughts are directed towards eating, cleansing the body and putting on neat dress. That is all. Even the so-called educated persons live in Annamaya Kosha only. Sometimes, they live in Manomaya Kosha (mental sheath). A spiritual aspirant with Viveka lives in Vijnanamaya Kosha (Intellectual sheath). The Vijnanamaya Kosha is developed by abstract thinking and reasoning, by systematic meditation, study of the scriptures. You must all develop the Vijnanamaya Kosha by the study of spiritual books and pure thinking. Then you are safe. Mind will stop to deceive and torment you.
Mind is absorbed in Intellect. Individual Intellect is absorbed in the Cosmic Intellect; Cosmic Intellect in Avyakta; Avyakta in Supreme Soul. This is the Laya-Chintana (Involution or Absorption) of Mind. Sambhavi Mudra, looking at the spot midway between the two eyebrows, looking steadily at the tip of the nose, hearing the sounds of the ear all belong to Laya-Yoga. By these practices the mind gets Laya soon. In Sambhavi Mudra, the eyes are open but the mind is fixed on the Target. The eyes do not see the external objects. When the mind and senses are thinned out and eventually controlled, the various activities of mind and senses ceases. Personality-notion and sensation vanishes. Existence remains.
The two kinds…
Annihilation of mind is of two kinds, viz., (i) Destruction of the nature of mind, as in the case of the liberation and (ii) Destruction of the very form of the mind, as in the case of where they leave off their physical bodies. The first is termed destruction of the mind with form. The second is termed destruction of the mind without form.
Mind – Its Mysteries and Control by Sri Swami Sivananda