Answer
Wa `alaykum as-Salamu wa Rahmatullahi wa Barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother, thank you for your question and for your eagerness to be more knowledgeable about such Islamic issues.
It should be known that executing in Islam can neither be decided nor carried out by any Islamic organization. Rather, that is to be done by the Islamic state and under very strict rulings. The punishment of execution is similar, in some way, to what is so called “grand treason” in modern ages.
In response to the question you raised, the European Council for Fatwa and Research issued the following fatwa:
Executing whoever reverts from Islam is the responsibility of the state and is to be decided by Islamic governments alone. Islamic organizations and establishments cannot make such rulings, nor can they carry them out.
In any case, a considerable number of our predecessors (Salaf) agreed that not all who revert from Islam are to be executed. Rather, those who declare their action in public and may cause fitnah by bringing down the name of Allah Almighty, His Prophet (peace and blessings be upon him) or the Muslims. The punishment of execution in this case is to protect and preserve the entire nation from the evil that this individual will undoubtedly bring, and is not a case of confiscating his or her rights of expression and belief.
Indeed, by committing such an act, the individual has transgressed upon the rights of others as well as the entire state and nation, which come before anyone’s individual rights. Modern legislation uses the term “Grand Treason” for crimes similar to the act of one who reverts from Islam then announces this in public and wages a campaign against Islam and the entire nation.
Allah Almighty knows best.