In the case of a mudslide sufficient to cause a major problem for the trains, the brawny crew of Irishmen would have been required, since once the mud was leveled (or removed) the tracks would need to be realigned and nailed back down.

In the few mudslides I've seen, all of the track was pulled up and relaid, since any movement of the rails (whether or not visible to the crews) would make it unsafe to move anything on them before they were cleared and intensely inspected. Just pushing the mud off would seldom be a sufficient "repair."

John