How do I mute the monitoring of an incoming signal during recording so I only hear pre-existing tracks?

Welcome to the forum.
Turn off Input Echo. It should be next to the MSR buttons.

You normally do this at your audio interface which will ether have front panel levels for the mix between "Computer/Input" or a software GUI mixer where you set your cue mix. 
Hopefully you own a audio interface. 
You should not attempt to record audio without a proper ASIO audio interface. It will not work very well. 
Your timing will be off.