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?
The nuke would melt before it could detonate if you were to drop it into liquid hot magma.
If you did somehow manage to get it in there without melting, it would vaporize the magma and blow a big hole in the mountain.