"Mute conversation" is a great thing, but I would love a "mute conversation starting from this toot" or "mute replies to this toot" (same thing) too.
There are long-winded conversations I find super useful, but they often have a branch or two that I could really do without.
I've made a reference to #Ecko by @weex in an issue I created earlier. See: https://github.com/magicstone-dev/ecko/issues/426
Note that one issue with muting is that you are still mentioned on the thread and you not responding to people directing to you may seem very impolite if they don't know you muted the thread fork.
@rysiek Oh yes, I've seen this too...