Salam I recently received a video which shows a man accused of rape ,being beheaded by a person with a sword, claiming that ‘this is the correct way to punish according to Islamic Shariat’. Is such punishment correct for punishing rapists? Are we Shias allowed to behead them? What is supposed to be their punishment? Wassalam. Regards from India .

Walaikumussalam
Punishment and enforcement of law and order it is the duty of the state and government.if we allow every individual can stand and enforce the law and order then this world become a horrible place. Islam means peace and another meaning is tasleem which means submission to the will of Allah.
These people and these type of the people they are implanted in ummah their aim is to defame the Islam.
Yes there is a ruling but there are the condition and only government and state has right to punish.
And among those condition only one point it should be witness by 4 Aadil people and their statement should me same and they all must witnessed the rape which is really hard to prove.
That video is absolutely against the Islamic teaching. Kindly do not share to anyone.
May Allah guide them and keep us remain on right path.
Aameen
Wassalam
Syed Abul Qasim Rizvi