A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
deu 13:1ENTICERS TO IDOLATRY TO BE PUT TO DEATH. (Deu 13:1-5)
If there arise among you a prophet--The special counsels which follow arose out of the general precept contained in Deu 12:32; and the purport of them is, that every attempt to seduce others from the course of duty which that divine standard of faith and worship prescribes must not only be strenuously resisted, but the seducer punished by the law of the land. This is exemplified in three cases of enticement to idolatry.
a prophet--that is, some notable person laying claim to the character and authority of the prophetic office (Num 12:6; Sa1 10:6), performing feats of dexterity or power in support of his pretensions, or even predicting events which occurred as he foretold; as, for instance, an eclipse which a knowledge of natural science might enable him to anticipate (or, as Caiaphas, Joh 18:14). Should the aim of such a one be to seduce the people from the worship of the true God, he is an impostor and must be put to death. No prodigy, however wonderful, no human authority, however great, should be allowed to shake their belief in the divine character and truth of a religion so solemnly taught and so awfully attested (compare Gal 1:8). The modern Jews appeal to this passage as justifying their rejection of Jesus Christ. But He possessed all the characteristics of a true prophet, and He was so far from alienating the people from God and His worship that the grand object of His ministry was to lead to a purer, more spiritual and perfect observance of the law.
deu 13:6WITHOUT REGARD TO NEARNESS OF RELATION. (Deu 13:6-18)
If thy brother . . . entice thee secretly--This term being applied very loosely in all Eastern countries (Gen 20:13), other expressions are added to intimate that no degree of kindred, however intimate, should be allowed to screen an enticer to idolatry, to conceal his crime, or protect his person. Piety and duty must overcome affection or compassion, and an accusation must be lodged before a magistrate.
deu 13:9thou shalt surely kill him--not hastily, or in a private manner, but after trial and conviction; and his relative, as informer, was to cast the first stone (see on Deu 17:2; Act 7:58). It is manifest that what was done in secret could not be legally proved by a single informer; and hence Jewish writers say that spies were set in some private part of the house, to hear the conversation and watch the conduct of a person suspected of idolatrous tendencies.
deu 13:12Certain men, the children of Belial--lawless, designing demagogues (Jdg 19:22; Sa1 1:16; Sa1 25:25), who abused their influence to withdraw the inhabitants of the city to idol-worship.
deu 13:14Then shalt thou inquire--that is, the magistrate, to whom it officially belonged to make the necessary investigation. In the event of the report proving true, the most summary proceedings were to be commenced against the apostate inhabitants. The law in this chapter has been represented as stern and sanguinary, but it was in accordance with the national constitution of Israel. God being their King, idolatry was treason, and a city turned to idols put itself into a state, and incurred the punishment, of rebellion.
deu 13:16it shall be an heap for ever; it shall not be built again--Its ruins shall be a permanent monument of the divine justice, and a beacon for the warning and terror of posterity.
deu 13:17there shall cleave naught of the cursed thing to thine hand--No spoil shall be taken from a city thus solemnly devoted to destruction. Every living creature must be put to the sword--everything belonging to it reduced to ashes--that nothing but its infamy may remain.