Muuter is a great tool to put a silencer on someone that is tweeting away at a conference you do not care about, or maybe some sports event. They make a good point of explaining if you unfollow someone, odds are you would forget to follow them back. Using this service gives you the needed break. They do the entire unfollow/follow action automated.
You are able to send a Direct Message to the service specifying who to silence and for how long. They utilize oAuth to engage the service and their actions do count towards your API usage. So beware of that. They do log every request they perform for you to review and act upon if necessary.
For a full FAQ see it here.