The Duelist - Thundercats (2011 Cartoon Network reboot)
From the fan Wiki:
About the Duelist
Nothing much is known about the Duelist other than he loves to duel to win famous and powerful swords. He keeps his collection within a shield that he wears on his back.
(Found by Google searching for "takes their swords".)
This was not an anime in the common narrower sense of Japanese animation, which initially made me hesitant to offer this as an answer, but as Wikipedia says, the reboot series "combined elements of western animation with Japanese anime", so it could easily be mistaken for a Japanese animation by someone less familiar with the series (and in any case, using "anime" to mean only Japanese animation is something of a Westernism).
A note for historical accuracy's sake regarding one other detail in the question: I'm doubtful it played on Animax. Wikipedia does not list it among programs broadcast by Animax and Wikipedia also does list it among the programs distributed in India by Cartoon Network India. (In a comment above, questioner mentioned that the recalled viewing occurred in India.) However, such a mix-up is easy to make, years letter.