No, there is no way to restart with the same character. Personally, I'd rather start a new game to try a different character build. There are different choices in side quests, etc, but where possible I save and do quests/conversations each way to see which is best, so there wouldn't be many changes if I restarted with the same character.
In the original release of D2:ED I played a duel wielding warrior, so for DKS I played a ranger (both with the Xbox versions). I'm not big on mages, so whenever I get around to building a new PC I'm planning on starting an unarmed warrior in DKS.
Welcome to the forum.