When the duke says of his last duchess that "all smiles stopped" (line 46), he implies that the duchess died. This impression is confirmed by the next sentence, in which he states, "There she stands / As if alive." He is describing, of course, the beautiful and lifelike portrait of the duchess that hangs behind a curtain in his gallery, and so the reader as well as the duke's actual audience in the text—the representative of the count whose daughter the duke now wishes to marry—understand that she has, in fact, passed away.

Moreover, prior to the duke's declaration that "all smiles stopped," he confesses that he "gave commands" which led to this effect, and this makes it sound very much like he had his wife murdered rather than explain to her that he wanted her to appreciate him more than anyone else or deal with the fact that she did not flatter him. In addition, he actually tells this to the person who is there to negotiate the potential terms of his next marriage. So, either the duke is so entitled that he thinks he was within his rights to have his last duchess murdered because she displeased him, or he is purposely letting the family of his next wife know that she'd better be ready to love him best (or at least act like it), or she'll get murdered too.