That's actually not true. When you cut/paste a file on your computer (for most computers), it's much faster than copying the file. Deleting the file is also not instant, so copy and delete should be the slowest of the three operations.

When you cut and paste a file, you're just renaming the file or updating the file database. It's different how that works depending on your file system, but it typically never involves rewriting much of the data of the file.

Edit: Fixed typo.