How to mute a video
Drop in a video and Mute is already on, so the copy you save has no sound track at all, rather than a silent one. Press Save video. To shorten it too, drag the handles on the strip of frames first; to keep the sound after all, switch Mute off.
The picture is encoded again
Leaving the sound out means writing the video again, frame by frame, with your browser's encoder, at the quality you set. So the file can come out bigger or smaller than the original; the line under the quality slider estimates it before you start, and the progress bar counts the frames as it goes.
Videos with no sound
If the video has no sound to begin with, the switch says so and stays off. At 0.5×, 1.5× or 2× the sound is left out anyway, since a change of speed would change its pitch.
Questions
Is muting instant?
No. A desktop app can drop the sound track without touching the picture; this page encodes the picture again, so a long clip takes a while. Trimming first makes it quicker.
Can I keep only the sound instead?
Yes, the other way round: drop the video into Extract Audio from Video to save just its sound as MP3 or WAV.
Can I mute just one part?
No. Mute takes the sound out of the whole clip you save; there is no way here to silence one stretch and keep the rest.