The Verge is reporting that a mute feature has started appearing in official Twitter clients for Android and iOS meaning that widespread use of the feature may be available in the near future. The mute feature would allow a user to stop the tweets and retweets of someone they follow from showing up on his or her timeline.
Muting would happen unbeknownst to the person on the receiving end, but direct messages between the two accounts and notifications would still be enabled. A mute would remain in effect until manually undone by the user as no expiration for the mute is able to be set. The feature gives Twitter users a way to skirt by social obligations to follow people without actually having to unfollow or block people whom they may not wish to see comments from.
Third party applications, including Tweetdeck before its acquisition by Twitter in 2011 and Tweetbot, have already implemented muting features within their clients. Tweetbot specifically allows for users to set a predefined time limit on the mute.
To see if the feature is enabled for an account, select the profile of the user you wish to mute and select the gear icon below the profile picture. If "mute @username" appears in the list then the account holder will be able to utilize the feature for the time being.
Twitter hasn't commented on the feature directly, but instead has directed people to a 2013 blog post in which company VP of engineering Alex Roetter states that "it's rare for a day to go by when we're not releasing at least one experiment."