Copying and pasting is a RAM hog, so if you are pushing the limits, then, yes you just may be running out of RAM space. But it should then move some to the system cache. This should be set to allow Windows to manage it.
As for using a external drives, they are so much slower than the internal drives. The USB interface has been known to be the source of many a programs access speed. The USB access uses the RAM and can also be a cause of running out of RAM.
I use good solid fast internal drives for my local data storage, and I use external USB drives for backup and transporting data. Most of my desktops have 2 or more internal hard drives. At times I have faster speeds across a network to a another machines internal drive than I do to a local external USB drive.