Finn killed innocent men, women, children, elderly without any provocation, that were not just executions or murders, that was an outright terroristic act. The Ark supporting and defending him to the last moment is unethical, by doing so, the Ark people undermined the U.S. constitution and U.S. Criminal procedures, and thus Ark people proved that there will be no hope for humanity if Ark people were to become the most dominant race on the Earth. Finn had to die. Blame Finn's death on the director/ scriptwriter who made Finn commit all those murders and earlier shoot to kill one of the grounders unprovoked in cold blood when others were ready to free him, they had already decided then and there that Finn needs to disappear from the series.
Clarke going to talk to Laxa to plead mercy for Finn was impractical. The entire clan was there to see the show of blood bath, get its revenge, Laxa was under pressure not to pardon him, otherwise the clan would have turned against Laxa herself and she might have lost her position or even life. There was no point by which Laxa could have pardoned Finn.