To me, Burns is saying that man's domination of the animals is both unjustified and harmful.
You can see that Burns thinks that this dominance is not justified from what he says in Stanza 2. There, he talks about himself as being a companion of the mouse -- they are both born of the Earth and therefore he is not better than it is.
He also acknowledges at length the fact that he has harmed the mouse with his plow. Stanzas 2-6 all have this idea in them to a greater or lesser extent.
Stanza 7 simply says that both mice and men have their plans destroyed by forces bigger than them.