John Gill Commentary Exodus 21:12

"He that smiteth a man, so that he dieth, shall surely be put to death." — Exodus 21:12 (ASV)

He that smites a man, so that he die
The Targum of Jonathan is, that smites a man or daughter of Israel with the sword; but there is no need to restrain the words either to persons of any certain nation, nor to any instrument with which a person may be smitten as to die: but any human person, man, woman, or child, of whatsoever nation, and they smitten with anything whatever, that issues in their death:

shall surely be put to death ;
by the order of the civil magistrate, and by the hand of such as shall be appointed by him; for this is the original law of God, (Genesis 9:6) .