Yes, you can move files on Mac without copying and dragging.
What you want is to move files on Mac, changing the file's locations on your Mac, instead of making a copy, there are some alternative ways you can choose:
Method 1. Run the mv command in Terminal. You need to launch the Terminal application from the macOS Utilities folder, then type the command mv file_path destination_folder_path, and press Enter.
Method 2. Use the right-click enhancer iBoysoft MagicMenu. It adds a Move To option to the Finder context menu, right-click the target item, choose Move To, and choose a location on Mac, it will move the selected item to a different location without copying and dragging.