Yes, Thragg kills Battle Beast in the Invincible comics. That is the short answer readers usually want, but the full context matters because the fight is famous for its brutality, duration, and unusual sense of fairness.
Note: this answer refers to the comic storyline.
Thragg defeats and kills Battle Beast after a long and punishing duel.
What makes the fight special is that Battle Beast refuses to accept an unfair advantage. After outside interference leaves Thragg badly injured, Battle Beast injures himself as well so the duel can continue on even terms. That decision is part of why the fight remains one of the most discussed battles in the series.
The battle becomes an endurance contest more than a quick clash. Both fighters keep forcing the issue, and the duel lasts long enough to become a serious proof point for how durable and dangerous each of them is.
In the end, Thragg survives and Battle Beast does not. That is why the answer to the search query is straightforward, even if the full battle analysis is much richer than a simple yes-or-no response.
Readers ask this question because the fight has a reputation that is bigger than the spoiler itself.
People are usually looking for one of three things:
If you want the bigger interpretation, the fight makes Battle Beast look elite while still leaving Thragg with the final victory. That is a major reason Thragg power discussions so often reference this duel.
Does Thragg kill Battle Beast?
Yes. Thragg wins and Battle Beast dies in the comic storyline.
Who wins Thragg vs Battle Beast overall?
Thragg does, though the fight remains one of the strongest showcases for Battle Beast as an opponent.
Why is this fight so famous?
Because it is brutal, prolonged, and treated by many readers as one of the best pure endurance duels in Invincible.