All forms of the death penalty administered by a Jewish court are mentioned explicitly in the Torah. And the death penalty by sword is a law that was given to Moses at Mount Sinai and is hinted to in the text, according the Maimonides. And any place where it is written alone מות יומת (shall surely be put to death), it means through strangulation.

And there is a difference between מיתה (death) and the rest of terminologies for death (like הכאה (beating), הריגה (manslaughter), etc.) in that the word מיתה does not indicate how one dies.

And any place where it is written דמיהם בם (their blood shall be upon them), it is referring to death by stoning. And this comes from the plural דמיהם (their blood), and from the language בו (upon him).

There are four types of death penalty that may be given by a Jewish Court, stoning, strangulation, burning, and death by sword. Stoning is the most severe type of death penalty and is the only type of death penalty which involves blood exiting from many places of the body. This is why the languageדמיהם בםin plural indicates death by stoning⁷³¹.

footnotes: ⁷³¹ Malbim, HaTorah v’HaMitzvah Kedoshim 103.