The speaker talks about a stone as if it were a well-mannered guest. It's "well-bred," dependable, useful for "any injury or sport," and ready to "go to bed" quietly. The humor comes from that polite, domestic tone, which treats a rock like a respectable member of the family.
Then the last two lines shift. The stone will go to bed "pretty as all the news / of war and sand." That comparison is unsettling. It suggests that news of war gets packaged in a tidy, pleasant way, and that we take it in calmly, then sleep. The word "sand" may hint at a distant desert conflict, though the poem doesn't say so outright, and it also echoes the sandstone of the title.
The mood is dry, wry, and slightly uneasy. The speaker doesn't shout. Instead, the calm voice and the blunt closing image make you notice how easily violence can be made to look neat and harmless.