The story is told briefly in the Panchavimsha Brahmana of the Sama Veda, and in more detail in the Jaiminiya Brahmana of the Sama Veda. Kutsa was the son of Indra, born from Indra's thigh. (That's why he's called Arjuneya, because Arjuna is a name of Indra.) He resembled Indra so much that even Indra's wife Shachi couldn't tell them apart. Once Kutsa had intercourse with Shachi, who thought it was Indra. When Indra found out, he made Kutsa bald, so they wouldn't resemble each other anymore. But then Kutsa wore a turban, and continued tricking Shachi. Then Indra made Kutsa's neck black with dust, but Kutsa wore a robe to cover it up. Finally Indra got really angry and wanted to put a curse on Kutsa, to turn him into a Malla (a type of mixed-caste), but Kutsa begged for mercy and Indra relented, making Kutsa a king instead. Once Kutsa became king, his first act was to ban all worship of Indra, to take revenge against Indra. But then Indra convinced a young Brahmana to make an offering to him, and then he bragged to Kutsa that he got an offering despite the ban. Kutsa got angry and killed the Brahmana. Then the Brahmana's father chanted a certain Saman (song) of the Sama Veda, which brought his son back to life. Here is how the Jaiminiya Brahmana of the Sama Veda describes it:
Kutsa Aurava ('sprung from the thigh') was formed out of Indra's thigh, just as Indra was, so was he: even as one who has been formed out of himself. Indra made him his charioteer. He (India) (once) surprised him (Kutsa) with his (Indra's) spouse, Shachi, the daughter of Puloman, and said to her: 'How hast thou done this?' She answered: 'I have not discerned you both.' He said: 'I will make him bald, in this way thou wilt discern (us).' He made him bald. But he (Kutsa), having covered his head with a turban, approached (her). This is the (origin of the) turban of the charioteer. He (Indra) again surprised him (with his spouse) and said to her: 'How hast thou done this?' She answered: 'I have not discerned you both, he has covered (his head) with a turban and so has approached me.' He (Indra) said: 'Between his shoulders will I strew sand, in this way thou wilt discern (us)'. And he strewed sand between his shoulders. That is the sand that is found between a charioteer's shoulders. But he (Kutsa), having covered it with his upper-garment, approached her. He again suprised him and said to her: 'How hast thou done this?' She answered : 'I have not discerned you both, he has covered himself with his garment and so has approached me.' He (Indra) drove him away, saying: 'Be a Malla.' He said: 'May we, o Indra, not go to ruin; give thou that to us by which we may live; from thee, forsooth, we are born.' (Indra answered:) 'Then shake thou off that sand between thy shoulders.' He shook it off and it arose as that great people called the Rajas and Rajiyas. Of them he was the king. His house-chaplain was Upagu, the son of Susravas. He (Kutsa) said: 'Let no one offer sacrifice. He who in my realm acts as offering-priest, must be deprived of his possessions. The Gods, forsooth, do not eat if no offering is made. Not even the leaf of a tree must be offered.' Now, Indra went to Upagu, the son of Susravas, and said: 'I pray thee to offer for me.' He answered: 'They do not offer sacrifice here; he who would offer, him they would deprive of his possessions.' He showed him the world (of heaven) saying : 'This world thou wilt gain, if thou offerest sacrifice.' He (Upagu) thought: 'Let them deprive me! Come, I will offer.' ... [Kutsa] rose and smashed him to pieces and scattered him in the water. But his father, Susravas, the son of Sthura, learned: 'Kutsa Aurava has smashed thy son to pieces and thrown him in the water.' He came running to him and asked: 'Where hast thou put my son?' He lays there smashed to pieces in the water.' He went after him in the water (to fetch his son). From out his mouth Indra in the guise of a rohita (fish) drank the soma. He thought : 'This forsooth, is Indra, him I will praise. He will revive this (son) of mine.' He saw this saman and lauded him with it (and then Indra revived his son).
The part at the end, by the way, is the whole reason this story is told in the Brahmanas of the Vedas; the story demonstrates that this particular Saman is a wish-granting Saman.