I wad be laith to rin an' chase thee, Wi' murd'ring pattle! (5-6)
The speaker's social class is announced in the title. He says that the poem is addressed "to a mouse, on turning up her nest with a plough." In other words, the speaker of the poem is a farmer ploughing his field. The opening stanza confirms this: the speaker refers to different parts of the plough (the "pattle" is the handle of the plough) and seems to assume that the reader will know what he means.
[…] thy poor, earth-born companion, An' fellow-mortal! (11-12)
The speaker compares himself to the mouse, saying that they're both "poor." But the word "poor" can mean both poor in possessions or money (as in, the opposite of rich), OR it can mean "worthy of pity or sympathy." The speaker might be using the word in both senses here—in any case, the idea of poverty is certainly introduced by this word choice.
I doubt na, whiles, but thou may thieve;What then? poor beastie, thou maun live! (13-14)
The speaker admits that the mouse probably steals the occasional bit of grain from the field, but he doesn't care—so what? he asks—"what then?" After all, the poor little guy needs to survive. Again, the speaker uses the word "poor" in both senses: it means both lacking in material possessions (since, after all, the mouse doesn't have any money in the bank) and it means that the mouse is worthy of our compassion or sympathy. But these lines are also important because the speaker personifies the mouse. After all, it's hard to call a mouse a "thief," even if he is stealing grain, because it implies a moral judgment. And the mouse is just a mouse. He's just doing what mice do. It seems like the speaker wants us to feel pity for the mouse, while he's also nudging us to think about how a poor person who steals a loaf of bread to survive might be worthy of the same kind of sympathy.