How do I make it so that when the "System deactived" pops up on the serial monitor after hitting my push button, it deletes the "System active Enter degree(s) 0-180." line and just displays "System deactived".
To do this, you need to use something other than the Serial Monitor that comes with the Arduino. What you use needs to understand something like VT100, and you need to include appropriate VT100 codes in what you send to make it clear the screen.
In a former job, I knew all about how to make VT100 screens do all kinds of cool stuff, but that was 25 years ago.