Arjun, the central character in the epic Hindu text Mahabharata, did not cut his thumb.
This question likely stems from a misunderstanding or a misremembered detail from the epic. There are many instances of self-sacrifice and acts of bravery in the Mahabharata, but none involve Arjun cutting his thumb.
It's possible that this question is based on a different story or legend, or perhaps a misinterpretation of a particular event in the Mahabharata.
To clarify, it's important to remember that the Mahabharata is a vast and complex epic with numerous characters and events. It's easy to misremember or misinterpret certain details.
If you have any more information about the context of this question, it might be possible to provide a more accurate answer.