In the first Austin Powers movie, Dr. Evil steals a 50 kiloton nuclear weapon, straps it to a drill and is going to fire it into the mantle to trigger volcanic eruptions world wide.
My instinct is that, compared to a lot of nuclear weapons in the megaton range, 50 kilotons is not really a lot, and using it to try to move rock (even molten rock) is not going to accomplish his goal. Would it even cause a measurable change in the pressure that far down?
I’ve seen the same question asked about Lex Luthor’s plot to sink California for a land monopoly in the first Superman movie. As others have said, the weapon yields in these movies aren’t nearly powerful enough to do more than register a small local quake, if that. Also, while the mantle (mainly lower part) is fluid in the sense that it moves, it is very dense, so liquid doesn’t always mean easier to move.