He killed her for the same reason he killed Kyle Butler. He's going after Dexter, and killing to hurt him & preserve his own secrets. It seems like the murder that hurt Arthur the most and got him started was the bathtub death of Vera, his sister. The murder(s?) of his parents were rage issues stemming from his messed up feelings about Vera & his role in her death. By killing Rita in the "Vera" death he was trying to hurt Dexter the same way. Vera is the death that haunts Mitchell, which is why he uses her ashes in his ritual and so on, and he is trying to scar Dexter in the same manner. Also, it was probably more convenient than dragging her to a building to make her jump.

As for the "when," in Season 5, the time of death is given as roughly the same time the raid on Arthur Mitchell's house was going down, so while the Morgans were in his house, he was in the Morgan house slitting Rita's leg open.