Can I disable the external graphics card without taking it off the motherboard?

First step will be BIOS, there's generally two options you'll be interested in.

The first one is graphic card priority, the actual name of the option will differ from machine to machine but it'll have options like:

PCI-E (or PEG) Onboard PCI-E/Onboard

For this one you want to select the option that shows both... the second option will generally be called something like Multidisplay and you want to enable that.

Between those two options you have both cards powering up and BIOS prepared to display stuff on both of them.

From there you can just go into Device Manager in Windows, right click disable the card you want to 'remove'