Albert Barnes Commentary Deuteronomy 21:23

"his body shall not remain all night upon the tree, but thou shalt surely bury him the same day; for he that is hanged is accursed of God; that thou defile not thy land which Jehovah thy God giveth thee for an inheritance." — Deuteronomy 21:23 (ASV)

He that is hanged is accursed of God – that is, “Bury him that is hanged out of the way before evening: his hanging body defiles the land; for God’s curse rests on it.” The curse of God is probably regarded as lying on the malefactor because, from the fact of his being hanged, he must have been guilty of an especially atrocious breach of God’s covenant.

Such an offender could not remain on the face of the earth without defiling it (compare Leviticus 18:25, 18:28; Numbers 35:34). Therefore, after the penalty of his crime had been inflicted, and he had hung for a time as a public example, the holy land was to be at once and entirely delivered from his presence. See Galatians 3:13 for Paul’s quotation of this text and his application of it.