Unlike Windows, the Cut option in Finder and Command-X can only be used to cut text instead of files and folders on Mac. That's why you attempt to cut a selected file/folder but the Cut option is greyed out or the Command-X key shortcut doesn't work.
Although you can't directly cut files/folders to another location on your Mac, some workarounds exist to move items there.
1. Select the desired item, and drag-drop it to the location within Finder.
2. Copy and paste items on Mac and then delete the original source.
3. Move files on Mac using the title bar.
4. Change file location by running Terminal commands such as "mv ~/Downloads/MyFile.txt ~/Documents/Work/MyFile.txt."
5. Move files to a selected path with iBoysoft MagicMenu's Send To feature in the right-click menu.