Can iPhone photos be cut, then pasted onto another photo?

If you are referring to the ability to lift the subject from a photo, you can’t put that lifted subject onto another photo in iOS. You can, however, find a third party app on the App Store that has this functionality.

You can do something like this:

1. Grab subject
2. Go to anywhere in photo library where you are viewing multiple photos (without clicking on one, and while still holding the lifted subject)
3. Let go after the green plus appears on the top right corner of the lifted subject. It should add the lifted subject to your photo library, without the background.
4. You can then use the photo in a third party photo editing app to put it onto another photo.