The polar opposite of Tetsusaiga is the sword Sesshoumaru inherited, Tensaiga. Forged from their father's right fang by Toutousai, Tensaiga is sword of life. Where Tetsusaiga can kill a hundred demons with one stroke, Tensaiga can save a hundred lives. If used by someone who's mastered it by learning to cherish others it can heal or even restore life.
To all outward appearances would make Tensaiga completely useless to Sesshoumaru. He seems so annoyed with it that he just carries it with him and doesn't even think to use it. The first time see him really use it is on Jaken, and all it does is knock Jaken to the ground unharmed. It doesn't cut, he can't even use it as a club, so what is it good for?
Defense, healing, and most incredibly, resurrection. When Inuyasha manages to fully execute a Kaze no Kizu on Sesshoumaru, Tensaiga put up a shield of light around Sesshoumaru that kept him from being killed. Tensaiga's truly remarkable power is resurrection, or more accurately, prevent death. When wielding Tensaiga, Sesshoumaru is able to see the pallbearers that have come to take a soul away and he is able to kill them with Tensaiga. Since the pallbearers are dead, the person's spirit returns and they're restored. I guess that makes as much sense as anything else going on.
Much later in the series Tensaiga demonstrates an ability to communicate with Sesshoumaru in a primitive manner. When Sesshoumaru is fighting the undead Jaguar demon, Tensaiga signaled that it wanted to be used by pulsing. Since Tensaiga is a healing sword and the Jaguar demon was undead, healing did damage to it, killing it in one stroke. Yeah, I know. It makes more sense if you've played RPG's where healing spells have the opposite effect on undead.
