To answer your question, yes, the Arduino/Due needs to be connected to a PC while you are cutting (running the GCode).
There are a few options for this like buying a laptop to keep near your Maslow. But with you saying funds are tight, you can go the route of a Raspberry Pi. You can search Raspberry Pi on the forum here and can find numerous posts (like this one) depending on which version of the Maslow you have (Classic or M2). All you would need then is a good internet connection, and you can then control it from your phone/tablet/desktop PC. IMHO, that would be your cheapest option. If you go with the RPi, I highly recommend you use a device that you can keep near the Maslow as you will want to be there to watch the machine as it is cutting and have a way to stop the program quickly if something goes awry!