A demon named Madan undertook austerities and won the boon of vak siddhi, according to which anything he said came about. He abused this siddhi by killing people. Enraged by his mischief, the gods worshipped Bagalamukhi. She stopped the demon's rampage by taking hold of his tongue and stilling his speech. Before she could kill him, however, he asked to be worshipped with her, and she relented, That is why he is depicted with her. She is almost always portrayed in this act, holding a club in one hand, with which she is about to strike her enemy, and with the other hand pulling his tongue. In this myth, by stopping the demon's tongue, she exercises her peculiar power over speech and her power to freeze, stun, or paralyze.
More than any of the other Mahavidyas, Bagalamukhi is associated with magical powers, which are sometimes referred to as siddhis, "accomplishments" or "perfections." Among her epithets in her hymn of a thousand names are She Who Gives The Eight Siddhis, She Who Gives Magical and Mystical powers (riddhis and siddhis), and She Who Gives All Siddhis. The invocation written around the edge of an amulet containing her yantra in the Tantrasara reads: "O Bagalamukhi, please arrest the speech of wicked people, paralyze their faces, fix their tongues and destroy their intellect." At the end of her stotra (hymn) in the Rudrayamala, it is said that those who worship her will be able to make their enemies deaf and dumb, destroy their intelligence, and turn their wealth to poverty.
This description by Nitin Kumar, Executive Editor, Exotic India.
Kinsley, David. Tantric Visions of the Diveine Feminine. New Delhi: Motilal Banarsidass, 1997.