How to delete an unwanted note or rest
You can delete rests from voices 2, 3 and 4. You cannot delete voice 1 rests. Music is either sound or silence. You can replace rests (silence) with notes (sound), you can remove sound (select note and press the del key) and get silence, but you cannot remove silence. Unless to replace it with sound.
If you want to remove a voice 1 rest or a note or chord and expect all following music to move left to fill the gap: MuseScore doesn't work that way, you'd have to use cut and paste instead.
You can however (as of MuseScore 3) use Ctrl+Del (Mac: Cmd+Del) to delete a beat (note/chord or rest) from a measure, creating an irregular measure. See also Remove selected range.
If you want to create an entirely empty measure, you can turn the voice 1 rest invisible: select it and use either V or untick the 'Visible' box in the Inspector's Element section.