How can I edit a m4v movie file and retain subtitles?

I made a copy of a DVD and two sets of subtitles (Hebrew and English). Both subtitles are optional and only VLC can display them. I am trying to edit out a scene of the movie. QuickTime can do this, but can also only save the file as a mov afterwards, which destroys the subtitles. When I edit and export to m4v, the subtitles are allegedly still there but even VLC cannot display them any more. How can I edit an m4v file with optional subtitles without destroying the subtitles?