In The Name of Allaah, The Most Merciful, The Bestower of Mercy.
Imaam Abdul Azeez Bin Baaz [rahimahullaah] said: As for stopping evil with the hand, this should be done where one has authority, such as one’s home [within what the laws of the country allows] with those under one’s responsibility, or those authorized by the ruler, such as organizations given permission and authority to enjoin good. They should make changes in accordance with the authority they have been given- in the way prescribed by the Sharee’ah, without exceeding their jurisdiction. The same applies to the governor of a city; he should make changes with his hand, in accordance with the instructions he has been given [by the government]. [Ref 1]
Shaikh Saaleh Al-Fawzaan [hafidhahullaah] said:
The ones who actually judge with apostasy are the legislative judges and those who are able and fit for giving legal verdicts. And as for those who enforce the judgements they are the leaders of the Muslims (wullaat al-amr). As for whatever is other than this, then it is mere confusion.
Meting out the punishments is only appropriate for the leader of the Muslims and it is not for every person to establish the punishment, since confusion, and corruption necessarily follows from this, and also the cutting off of the society, tribulations and provocations occur. Establishing the punishments is appropriate (i.e. befits only) to the Muslim leader.
And from the responsibilities of the Sultaan in Islaam, and from those matters that befit him is the establishment of the punishments after they have been established legislatively, via the Sharee’ah law courts, upon the one who fell into the crime for which the legislator has designated a specific punishment, such as for stealing. So what has been said is that establishing the punishments (i.e. meting them out) is from the rights of the Sultaan, and when the Muslims do not have a Sultaan amongst them, then they should just suffice with commanding the good and forbidding the evil, and calling to Allaah, the Might and Majestic, with wisdom, good admonition and arguing with that which is best. And it is not permissible for individuals (in the society) to establish the hudood, since that, as we have mentioned, will bring about chaos, and also provocations, and tribulations will arise, and this contains greater corruption than it contains rectification. And from amongst the Sharee’ah principles that are submitted to is, ‘Repelling the harmful things takes precedence over bringing about the beneficial things’. [Ref 2]
[Ref 1: Fataawa Ibn Baaz 8/208. Slightly paraphrased]