No execution by hanging.
This verses study is a typical example of law learned from the 13 midot.
See Mishna and Gemara Sanhedrin 45b. In mishna two views, Rabbi Eliezer said that all who were stoned should be hung. Chachamim said that the blasphemer and the idolator.
Gemara explains that both read the verse 23, in which is written because the curse of G-d is upon him.
Chachamim use a drasha called "Set and item" "he would be killed and hung" described the set of all the sentenced to death but "curse of G-d" described a particular item only. In this case the Torah refers to the item only.
Rabbi Eliezer said that the item/s defined a sub-set, all the condemned to stoning. He learned the verses following an other tradition of study, called "adding and subtracting".
You can learn from this Gemara three rules
Nobody is killed by hanging,
Hanging is only for someone who is killed because of blasphemy or idolatry according to Chachamim
According to Rabbi Eliezer all stoned and stoned only.
If he was not Jewish his condemnation is only by strangulation (Sanhedrin 57b). according to Rabbi Eliezer he would not be hanged but according to Chachamim maybe that if he was condemned because of blasphemy or idolatry he would be hanged after the killing .
Concerning the fact that Tora said that his body is promptly removed, this rule is in verse and in Mishna (see Sanhedrin 46a) concerning each man who was hanged by Bet Din.
HE IS IMMEDIATELY AFTERWARDS LET DOWN.
IF HE IS LEFT [HANGING] OVER NIGHT, A NEGATIVE COMMAND IS THEREBY TRANSGRESSED, FOR IT IS WRITTEN, HIS BODY SHALL NOT REMAIN ALL NIGHT UPON THE TREE, BUT THOU SHALT SURELY BURY HIM THE SAME DAY FOR HE IS HANGED [BECAUSE OF] A CURSE AGAINST GOD, - AS IF TO SAY WHY WAS HE HANGED? - BECAUSE HE CURSED THE NAME [OF GOD]; AND SO THE NAME OF HEAVEN [GOD] IS PROFANED.
note: There are therefore more opinions. E.g. In Gemara 56a Berayta said that non Jewish are prohibited from blasphemy and killed by beheading. So for RE there is no stoning, thus, no hunging. For Chachamim maybe hunging.