Cutthroat: Does it Silence existing skills/buffs?

Basically what I'm asking is if the barbarian has their shouts/achilles up already, and I hit them with cutthroat, will they go away? Or is the idea to run it with ambush to prevent phantomize/etc after the fact.

Also if a wizard or cleric is in the middle of channeling a spell, can they still let it go, or does it just stop working?

Thanks