In previous versions of QuickTime you could remove the audio track and save the file. This function appears to have been removed in QuickTime 10.
Is it still possible?
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What you are looking for is a demultiplexer or demux utility. Which one to use can depend on your specific file container format.
Avidemux is an opensource tool for Mac/Win/Linux that does the job. Load your file, and in the Audio menu pick Choose Audio Track, then disable the audio track, and save to a new file. Make sure Video stays on copy.