It has to be formatted to the OS HFS+ for Mac/NTFS for Windows. However I'm not sure Photoshop can "see" an SD card slot, so try a SD to USB adapter if Photoshop doesn't list it in your scratch options.
A terrible idea. What is the fastest SD card available? 100Mb/s with the wind behind it, and providing you have a really good card reader. I am sure that reading and writing to scratch files is a serious bottleneck, and it gets worse if you use a lot of Smart objects. If you really need to use an external drive for scratch space, look at a USB3 drive that comes with its own power supply, like the Seagate Expansion. They are good for 180Mb/s.
But let's take a step back. Have you really run out of space, or is there another problem?
How much free space does the primary Scratch drive have?
Look for orphaned Photoshop temp files in the root of that drive. If it does not have today's date, delete it. Or close Photoshop, and if any are left, delete them.
If you just have the one drive, then you might be able to free up a bunch of space. If it was a Windows system, I'd suggest WinDirStat to see what is clogging the drive, but there is a Mac equivalent. You'll need Gene or another Mac expert to suggest what can go, but the best plan is to relocate some things to a second drive. Your
Whoops.. Just read your post again and I see you are using a Surface Pro. I have to go cook our tea right now, but'll post gain later if no one else has sorted you out.
OK, so you are using Windows, and I imagine Windows 10?
Download an install WinDirStat, and check your boot drive.
It will produce something like this, and you need to look for the big chunks of data, like the huge blue rectangle in the middle of my screen shot.
If I click on that blue rectangle it tells me it is Windows hibernation which is 25Gb on my system, and something you don't need. So disabling it would immediately win me 25Gb of space and it's a PITA anyway. The only reason I have not disabled so far on this system is that I have a 500Gb boot drive, but I have noticed that I can't wake Photoshop from Hibernate, so will be getting rid soon.
There are lots of opportunities to reduce space on a Windows 10 boot drive, and a ton of links telling you how:
While it is a terrible idea to use your SD card as Scratch space, there is no reason not to 'mount' it as a normal drive, and move some of the non-critical data to it. If you are not, please feel free to run it buy us, but things like old picture files and other documents, downloads etc. I don't actually know if you can hot swap an SD card when it is mounted, but if you can, then it would be a great way to do your backups.
Yes, WinDirStat will quickly become essential - keep the link handy everyone! There will be a rush of these coming!
All those first-generation 120/240 GB SSD machines are now starting to hit the wall. It worked for a while, but now the user account folder has accumulated enough junk to fill the system drive up completely. A lot of users will be at 80% or 90% by now.
After running Windows Disk Cleanup, the only sensible thing to do is to clean out the user account. Look for caches and preview folders. This is where WinDirStat is indispensable - those big folders stick out and you see them right away.
As an emergency first step - delete all Bridge Previews, going back all previous versions you have had installed. Redirect the previews folder to somewhere else in Preferences. If you have Premiere Pro and After Effects, they are other big offenders. Do the same there.