I don't think you can kill a totem spirit directly. In fact, in Street Grimoire it's pretty specific that you cannot target a totem spirit, and often times those that don't follow a totem spirit can't even sense the spirit at all. Which makes me wonder: how would you kill a totem spirit? Or perhaps more precisely, what is a totem spirit? It doesn't follow the normal rules for a spirit at all (can't be bound, can't be summoned, can't be attacked, can't be sensed, etc.) and yet it's almost universally referred to as a spirit. People make pacts with their totem spirits, they can summon ally spirits that are aligned with a totem, and some other things that seem... spirit-ish.
My take on it is that the totem "spirit" is a creation of astral energy that reflects ideals and concepts. This would make them spirits in some regard, but I would argue that they can't exist without people who believe in them. For instance, Coyote. The coyote animal is not actually a trickster or anything special. So the Coyote totem does not reflect the coyote animal at all - instead it reflects the ideal of trickery. It only appears as Coyote to those that believe in Coyote. It could just as easily appear as Clown, Raven, or just Trickery as a pure ideal. These manifestations can take thousands of guises, but never actually enter our world. Thus the spirit isn't a true spirit, but rather a concept given astral form and power.
Thus, I believe that a totem spirit is not a spirit at all, but it can be subject to some of the rules of a spirit. If one wanted to "kill" a totem, they'd have to kill the ideal that the totem represents. Some of these ideals or concepts are rather convoluted though. Dragonslayer for instance is a hero - how does one kill the concept of heroism in the world? It's ingrained into the very fiber of our being.