"Who'd stoop to blame this sort of trifling ?" - What does the speaker mean by ?

The Duke is alluding to the fact that he'd like to reprimand her for her actions, but after thinking about it considers himself "too good to reprimand," and that there's no reason he should have to. The Duchess should know her place without having to be reminded. You might want to look this over in context, simply looking at one small snippet affects the way you understand the entirety.