If a competitor in a challenge is riding a mount, then that mount (including the crew of a chariot, if the character is riding one) must direct its attacks against either the other competitor or that competitor's mount (if he is riding one). If the opponent is slain before all of a model's attacks are made (because a competitor and his mount strike at different Initiative steps, for example) then any excess Attacks are lost and cannot be directed against other models.
Excess wounds caused against mounts count for the purposes of overkill. If a character is slain but his mount is not, the mount will (after taking its Monster Reaction tests) continue fighting in the challenge until it or the foe is slain (or flees).