How to Move Files Without Copying Them?

I have Mac Pro (Early 2009) with Yosemite 10.10.5.

When I move a file or folder with the computer mouse from the computer desktop, for example, the file or folder is copied to the new location while the original file or folder stays in place.

Thanks for any tips on how to move a file or folder with the computer mouse "without" also copying the file or folder at the same time.

The default behavior in OS X is to move files/folders on the same machine. You can prevent this by holding down the Option key to make it copy. Copying files to external devices is a copy by default..

So technically, you seem to be experiencing the opposite of how things should be working..

You mention Desktop as one folder, where is the other folder?