So a game that i decided to run is filled with copyrighted music. Am i able to submit it? Or do i just take out the audio all together?

Run videos aren't hosted on the site, so it comes down to what video service you use.

If the video is partially (or even fully) muted, it shouldn't matter, though that's up to the game's community to decide for sure. If it's a local recording being upped to YouTube, I don't think there will be any issue, at least not with muting (you might have ads appear on the video and you will not be permitted to monetise it, but that's all secondary to just having it in the first place).

I actively avoid the issue by changing settings. There's a game I run, Star Wars Racer, where a piece of music triggers a copyright notice, meaning they put ads on the video. It's just a crappy MIDI version on the N64, but that still seems to be enough for those scumbags. As a result, I turn off the music in the games settings for every run I upload to Youtube, so they can't profit off me. Twitch doesn't seem to care about the music.