Don't want to unfollow someone on Twitter? No problem, Twitter's got you covered. The company started rolling out a "mute" function this week that lets users block tweets from specific users they follow, but still see any mentions or @reply messages from that person.
In effect, it lets you unfollow someone without letting them know. It effectively removes all of that person's content from your own Twitter timeline, but doesn't break the "following" connection between you and that person. It's not as harsh as either a "block" or "unfollow."
Muting someone will allow that person to continue interacting with your tweets by retweeting them, replying to them and clicking the "favorite" button. If you blocked them, which is a function Twitter has long allowed, they wouldn't be able to follow you or interact with your tweets.
When you mute someone on Twitter, they do not get notified or have any way of knowing you have done so. It's a lot like how Facebook allows you to hide content from certain friends in your news feed.
To mute someone, click the "more" button next to their tweets, and then click "Mute @theirusername." You can also mute from a person's profile page by clicking the gear icon at the top of the page and doing the same thing in the drop- down menu.