As things currently stand, save data can not be moved off of the Nintendo Switch console despite other options included in the system’s settings to allow for other data to be moved between multiple consoles.
Yes, the day-one-patch did indeed add features, but it did not address the save game situation. You still have some control over your save files, such as deleting them. But that is about the extent of your power.
This issue is rather frustrating, as a handheld console has a higher chance of accumulating damage through transit, or theft. Imagine you’ve clocked over a hundred hours on Zelda: Breath of the Wild and suddenly your console gets stolen? What are you supposed to do?
Hopefully it is something that will be fixed eventually. Something like a cloud backup feature linked to your Nintendo account, or copying save-data across microSD cards would be nice (Nintendo, if you’re reading this).