This feature is available since version 12.95.0.
Thread Mute mutes the thread of a given note. This includes all replies connected to the uppermost note.
If you mute a thread, you will no longer be notified of new replies to that thread, nor will any of the replies mention you.
To mute a thread in Misskey Web, open the menu of any note belonging to the thread in question or the note from which it originated and select 'Mute Thread'.
The entire thread will be muted, regardless of which note in the thread the mute operation is performed from.