to stone someone: to kill, or try to kill, a person by throwing stones at them, the public execution the Law of Moses prescribed
This verb names a specific, deliberate act, not a casual throwing of rocks: a crowd putting a person to death by pelting them with stones. Under the Law of Moses stoning was the standard public execution for certain crimes, carried out by the whole community, so the word almost always carries the weight of a formal death sentence rather than a spontaneous scuffle.
Nearly every use in the New Testament fits that pattern. Jesus twice grieves over a Jerusalem that "stones the prophets" sent to it (Matthew 23:37; Luke 13:34); the crowd puts Stephen to death this way (Acts 7:58); a mob plots the same fate for Paul (Acts 14:5); and both the Law's penalty for adultery (John 8:5) and the warning at Mount Sinai that even an animal touching the mountain would be stoned (Hebrews 12:20) use it. Even in Jesus's parable, where the owner's servants are abused rather than all killed, the violence is deadly serious (Matthew 21:35; Mark 12:4).
Greek has a close partner verb, λιθάζω, that means the same thing, and the two are used almost interchangeably; a fuller form, καταλιθάζω, simply adds the sense of stoning someone thoroughly. Hebrew likewise had two verbs for it, סָקַל and רָגַם, which the early Greek translators of the Old Testament often rendered with this very word.