All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
We have already given a comprehensive response to this misconception in Fataawa 89484, 89471 and 85488 and quoted the interpretations of the scholars of verse 2:256, so please refer to them.
As regards the verse in which Allaah Says (what means): {Indeed, those who have believed then disbelieved, then believed then disbelieved, and then increased in disbelief — never will Allaah forgive them, or will He guide them to a way.}[Quran 4:137], there is no relevance between the meaning which you understand from this verse and the correct meaning stated by the Muslim scholars. The meaning of the verse is that Allaah will never forgive the people who persisted in disbelief and that He will not guide them to the straight path.
As a matter of fact, Ash-Shawkaani said: 'Allaah informs us about this group who have believed, and then disbelieved, and then believed, and then disbelieved, and then increased in disbelief, that Allaah will never forgive them, neither will He guide them to a way which will enable them to find the truth or do good, as it is most unlikely that they will be sincere to Allaah and truly believe. This is because of their wavering, sometimes they claim to believe, and sometimes they apostate from Islam, and return to their disbelief and constant denial. Clearly, this is an evidence that they are playing with the religion, and have no correct or sincere intention…'
Some scholars interpreted the verse to mean that once a disbeliever embraces Islam his prior disbelief is forgiven for him, but if he apostates and disbelieves again, then, in this case, none of his prior disbelief will be forgiven. Al-Qurtubi said in his Tafseer (interpretation of the meaning of the Quran): 'It is said that Allaah does not forgive any disbelief, so how come Allaah Says (what means): {Indeed, those who have believed then disbelieved, then believed then disbelieved, and then increased in disbelief — never will Allaah forgive them.}, the answer for this is that when a disbeliever embraces Islam, his disbelief is forgiven, but if he disbelieves again and apostates, then, in this case, none of his prior disbelief will be forgiven. 'Abdullaah narrated that the Prophet was asked: ''Will we be held accountable for the evil we did in the Jaahiliyyah (pre-Islamic era of ignorance)? He replied: ''Whoever amongst you excel in Islam [i.e. be true to his commitment to Islam] he will not be held accountable for it, but whoever does evil after becoming a Muslim, he will be held accountable for both, the time of Jaahiliyyah and the time when he became a Muslim.''; another narration reads: ''…and whoever does evil in Islam, he will be held accountable for the first [Jaahiliyyah] and the last [Islam].'' To do evil here means to apostate.
Therefore, it is now clear that this verse has nothing to do with what you mentioned in your question.
With regard to killing an apostate, this is something which is confirmed by many other evidences.
Allaah Knows best.