How can I delete photos from my iPhone and still retain them on my desktop (OS X El Capitan)? I am not sure if it is possible to delete from my iPhone once the photos are on my desktop.
I suggest you to firstly disable My Photo Stream then sync your iPhone with your Mac library (using cable for instance).
In this way you can keep update the photos in your library by importing recent photos from iPhone and at the same time you can remove the pics from your iPhone without losing the copy pic in the Mac.
When using the iCloud Photo Library, all of your photos are synced between all of your devices. You cannot delete on one, and keep on another... basically, they all use the same library so they need to be in sync.
There are other options... such as exporting the photos from the Photos app on the Mac, and then deleting the photos from the library all together... but you cannot delete the photos on one device without deleting from all devices (when you are using iCloud Photo Library)
This might not be the answer that you are looking for, but if you use the third party Google Photos app there is a feature to delete the local copy of a single photo(or group of photos) from your phone while still storing it in the cloud. Google Photos can also automatically download your cloud library to your mac's hard drive, which could help you keep them on your mac. Google Photos has drawbacks of its own, but it is a good solution to this problem.
One suggestion I would have is to set up a shared feed (aka using the sharing button) and post any photos you want to keep to the feed, with you as the only recipient.
You can delete the photos off the phone -- the feed is unaffected. The photos will come up in Photos in it's own section based upon the name you called it.
However, I'm not sure, whether photos Imported into Photos are subjected to being deleted if you delete from the phone. As stated, Exported photos are ABSOLUTELY safe -- they are saved on your computer.
The only plus is, even if you mess up and do delete a photo you didn't want to -- it's a non-destructive delete -- you have 30 days to change your mind.
If you have an iCloud account and have My Photo Stream enabled they should sync right to your iCloud. After they are synced to your iCloud, you can then transfer them throughout your computer so they will be saved to your computer directly and not your iCloud. You can then delete the ones off your phone.
I had the same issue! My ICloud storage was full and I could not delete pictures from my iPhone or Mac without losing them completely. I figured how to clear up this issue, you have to remove your "documents and Desktop folders" from Icloud storage..on your Mac go to settings, iCloud,click options next to iCloud Drive, uncheck Desktop and Documents folder, this will remove everything from your desktop and in your documents folder so make sure you drag all of your important documents over to ICloud before you complete this step. Once the desktop and documents folder is removed from Icloud, drag all your important documents back to your desktop, add a "photos" folder to your desktop for your photos and Transfer all of your photos from your photo app on into your new "photo" folder. You can now delete pictures off of your iPhone and the photo app and still have them safe on your desktop. Hope this helps!!