The line in question simply means that the Duke ordered his wife killed. Now he is looking for another wife, and the person he is speaking to in this dramatic monologue is a representative of the father of the young women he is arranging to marry. He is showing this visitor his art collection, which includes a portrait of his former wife. A nobleman of the Duke's status had the power to have people killed in the period in which this scene occurs. It is shocking to think of a man having his wife murdered because she was too kind and loving, but that is what this proud, selfish, wicked man did. In Dante's Inferno the poet encounters Francesca da Rimini in a circle of hell reserved for adulterers, and she and her lover, the husband's young brother Paolo,tell him how they fell in love and were murdered by Francesca's husband, also a powerful Italian nobleman. This scene was commemorated by Tchaikovsky in a beautiful tone poem titled "Francesca da Rimini." "My Last Duchess" by Robert Browning is the most famous of his dramatic monologues and also the most frequently anthologized of all his poems.
My interpretation of the end part; Then all the smile stopped together, was that he killed her and then she couldn't smile. I think that people also had gotten a bit upset about her having been executed. My initial thought was that the Duke had the Duchess killed because she was a smiley person who was much loved in society and he killed her for what? All to become a picture for him to look at?