Hi Katie,
maybe that feature has been introduced with QuickTime 10.5 which is available from Mojave (10.14) above.
I've checked on a Yosemite machine (10.10) which carries QuickTime 10.4 (the same as yours) and indeed the audio/video remove commands aren't available.
You can remove audio track using a utility like Subler. Remember to make a copy of your video first and work on the copy.
There's even an Automator action for that, although some users claim it's not working properly: https://apple.stackexchange.com/questions/238653/remove-audio-track-in-quicktime-10
On Catalina the specific action has been removed from Automator, so I couldn't try.
On Yosemite it's available. I got actually a strange error, though – something protection-related (not possible to edit/modify the video).