We’ve updated Micro.blog’s muting today to work more consistently everywhere, with a new option to hide replies that mention the username you are muting. Now when you mute a username you’ll see an additional checkbox to enable this option:
Posts that would normally appear in any of the Discover screens or search are now hidden. Replies in the timeline and conversations are also hidden.
The muting interface is on the web under Account → Edit Muted Users. I’ve also updated the API to support muting.