to stone someone: to throw stones at a person in order to kill them
This verb names one specific act: pelting a person with stones so that the stones kill them. It is built on the ordinary Greek noun for a stone (λίθος), and in the world of the New Testament stoning was not random violence but the community's own way of putting someone to death, the penalty the Law of Moses set for offenses such as blasphemy. The word therefore carries the weight of a killing that a crowd carries out together, each person's hand in it.
Every New Testament use describes stoning that people attempt or suffer rather than a sentence a court has properly handed down. Three times in one scene a crowd in Jerusalem picks up stones for Jesus, and he asks which good work they are stoning him for (John 10:31, 32, 33), a danger his disciples remember when he proposes going back to Judea (John 11:8). The temple guard brings the apostles in gently because it fears being stoned by the people (Acts 5:26). A mob at Lystra stones Paul and drags him out of the city for dead (Acts 14:19), an experience he later counts among his sufferings (2 Corinthians 11:25), and the roll call of faithful sufferers in Hebrews says of some of them simply that they were stoned (Hebrews 11:37).
Greek has a second verb for the same act, λιθοβολέω, which is the one the Greek Old Testament prefers when it translates the law's death penalty, and a fuller form, καταλιθάζω, which stresses stoning someone thoroughly. They mean the same thing, so the choice between them is a matter of a writer's style rather than of sense.