The spear his mother gave (the Vel on the Pusam star)
Surapadman and his brothers hold boons from Shiva and enslave the gods. Shiva makes his grown son commander, and on the full moon of Thai with the Pusam star Parvati gives him the Vel, her own Shakti in the shape of a leaf-bladed lance, to destroy them. The boy takes leave of his mother and marches south with Veerabahu and the hosts; the war at Tiruchendur is told elsewhere. The Tamil poets and temples keep the Vel as a god in itself.
The asuras Surapadman, Tarakan and Singamukhan win boons from Shiva that make them all but unkillable, and Surapadman tyrannises the gods. Murugan, born of Shiva's six sparks and gathered into one by Parvati, is made commander. Parvati gives him the Vel, charged with her own power, on the day the Pusam star stands with the full moon of Thai, and he goes south to destroy the three asuras; Thaipusam is kept for that day. The Vel is held to be Shakti and spiritual wisdom, and Jupiter, giver of wisdom, rules the Pusam star. The same temple article says Thaipusam is also the day of Shiva's Ananda Tandavam at Chidambaram.
In the Mahabharata's Shalya Parva the gods install Skanda as their general and give gifts: Indra a dart and a banner (the dart is later called Agni's), Shiva an army of thirty thousand, Vishnu a garland, Uma two cloths bright as the sun, Ganga a water-pot, Brihaspati a staff, Garuda a peacock, Aruna a cock, Varuna a snake, Brahma a deer-skin. In the Skanda Purana's Kaumarika Khanda Kumara is made commander, Vishnu urges him on the seventh day to kill Taraka before sunset, he hurls the Shakti at the asuras, hesitates over a devotee of Rudra, and pierces Taraka's chest with it; afterwards he installs lingas in atonement.
What is different here:
The enemy is Taraka, not Surapadman; the weapon is the Shakti, hurled, with no scene of a mother's gift, and the Mahabharata's named projectile is a dart from Indra or Agni.
South India · Tiruvannamalai; Nallur; Tank RoadKaumara🪔 Thaipusam
Arunagirinathar of Tiruvannamalai, about 1370 to 1450, is said to have woken from a vision with the Vel and the peacock marked on his shoulders; his Kandar Anubhuti opens with the Vel and invokes it in 25 of 51 verses, calling it the Sakti Vel that pierced Surapadman and his kin and the Krauncha mountain, and his Kandar Alangaram sings the shining lance hurled at Surapadman and the Krauncha hill. He gave the Vel ten songs of its own, the Vel Virutham, beside eleven each to the peacock and the cock. Commentators read the mountain as karma and Surapadman as ego, which only the Vel of wisdom cuts. At Nallur in Jaffna the sanctum holds the Vel alone; in Singapore the Thaipusam walk ends with milk poured over the vel; devotees chant the Vel's victory, and Sri Lanka keeps a second Vel festival, Adi Vel, in July or August.
What is different here:
Not a narrative but the Vel as an object of praise and worship in itself.
Sources: Thaipusam, Wikipedia; Vel; Subramaniya Swamy Temple, Tiruchendur, Wikipedia; Idumban and the Palani hill as the temples tell it (Srikanda Swamy Kovil, Thaippoosam article; magikindia, Palani; Green Message, Palani); Mahabharata, Shalya Parva section 46, Skanda's installation (Ganguli translation, ibiblio); Tarakasura, Wikipedia (the Skanda Purana Kaumarika Khanda account); Skanda Purana, Kaumarika Khanda chapters 32 to 36, summary (Green Message); Arunagirinathar and the Vel (Kaumaram.com: Kandar Alangaram 49, Kandar Anubhuti 4 with N. V. Karthikeyan's commentary, the works list, the Esoteric Anubhuti introduction; Arunagirinathar, Wikipedia); Nallur Kandaswamy Temple, Wikipedia