I doubt na, whyles, but thou may thieve; What then? poor beastie, thou maun live!
The speaker says that he's sure the mouse steals to make a living.
He uses a double negative: "I doubt not […] but thou thieve." ("Na" is Scots for "not.")
But so what? says the speaker. He excuses the mouse's thievery with friendly sympathy. He calls him a "poor beastie," and says that the mouse has to live somehow, after all.
More translation from the Scots: "maun" means "must."
A daimen-icker in a thrave 'S a sma' request: I'll get a blessin wi' the lave, An' never miss 't!
An occasional ear of corn ("daimen icker") out of a bundle of 24 ears (a "thrave") isn't much to ask.
The speaker says that he'll get an extra blessing on whatever is left (the "lave") and he'll never miss the occasional bit that the mouse stole.
This seems very generous of the speaker… he's the one the mouse is stealing from (it's his field of grain, after all), and he says he doesn't mind if the mouse steals the occasional ear of corn from it.
The speaker already said that he felt like he had something in common with the mouse—they're both poor and they're both mortals. Hmm. Could the speaker be making a point about how poor people are treated? Let's read on…