Siegebreaker is purely a melee fighter, with a avalanche of a charging attack and a three-hit, punching attack that deals horrifying damage with the huge blades on the back of his hands. He has some sort of stomp or trample attack as well, one that tears up the earth and creates clouds of smoke from the earth in front of him.
There's no confirmation from Blizzard, but the consensus amongst players is that these interesting moves were not special one-hit kills, but were simply coded as interesting alternative graphics. The Barbarian and Witch Doctor must have been very low on hit points, to the point that the next hit was going to kill them. So, rather than them just falling over dead, Blizzard included some special code on Siegebreaker that enables him to show off a special fatality move when one of his attacks does enough damage to cause a player death.
That conclusion just begs another question, though. How many such special animations are there? Do all the bosses have some special fatality move they only show when they kill a character in a special way? Do any regular monsters have such talents? Do players die in as wide a variety of ways as monsters? Shattering when frozen, falling down and burning to a cinder from flame, charring to a skeleton from lightning, etc? Hardcore players might want to try out some softcore, just to run around and die in interesting ways.
Another interesting trick of Siegebreaker's is his death animation. He crumbles down to pieces in a very pretty way, like a decaying, hollowed volcano, but then sends out five jets of red light, which swirl around the screen for a moment before crashing to earth. Where the lights land, in the cemetery where the battle took place, great numbers of skeletons spawn. It's not clear why a giant centaur-dog beast like Siegebreaker would spawn human skeletons when he dies, but it is certainly a cool effect.
See screenshots and concept art of Siegebreaker in the Image Gallery.