There is no doubt that the Biblical teachings (particularly in the Old Testament, which is the Word of God according to both Jews and Christians) are explicit on the capital punishment for apostasy. The following Bible verses call for the killing of apostates and heretics.
2 If there be found among you, within any of thy gates which the LORD thy God giveth thee, man or woman, that hath wrought wickedness in the sight of the LORD thy God, in transgressing his covenant,
3 And hath gone and served other gods, and worshipped them…
5 Then shalt thou bring forth that man or that woman, which have committed that wicked thing, unto thy gates, even that man or that woman, and shalt stone them with stones, till they die. (Deuteronomy 17:2-5, KJV)
6 If thy brother, the son of thy mother, or thy son, or thy daughter, or the wife of thy bosom, or thy friend, which is as thine own soul, entice thee secretly, saying, Let us go and serve other gods…
9 But thou shalt surely kill him; thine hand shall be first upon him to put him to death, and afterwards the hand of all the people.
10 And thou shalt stone him with stones, that he die; because he hath sought to thrust thee away from the LORD thy God… (Deuteronomy 13:6-10, KJV)
1 If there arise among you a prophet, or a dreamer of dreams, and giveth thee a sign or a wonder,
2 And the sign or the wonder come to pass, whereof he spake unto thee, saying, Let us go after other gods, which thou hast not known, and let us serve them;
3 Thou shalt not hearken unto the words of that prophet, or that dreamer of dreams…
5 And that prophet, or that dreamer of dreams, shall be put to death... (Deuteronomy 13: 1-5, KJV)