First of all, speed is a relative term. What’s your current speed? Generally, Ethernet cable is the best way to connect to any networked device. Whenever cabled connection is available, use it! But it sounds like you’re already doing the right thing.
As for cutting files, that might depend on the method of access. But you can never just “cut files to the cloud”. You cut files at the source, and you paste them at destination. If that’s not a copy operation then I don’t know what is.
Cutting and pasting files on an internal disk drive is the equivalent of moving files within the local filesystem. But cutting and pasting files across the network is the equivalent of copying files. You’re duplicating the raw file data. The NAS device must create a new file in its own filesystem and save the paste data to it.
Try drag and dropping some files between two volumes in Windows with and without the Shift key pressed down and observe how it behaves. Dragging a file from C:\Foo\ and dropping it at D:\Bar\ is a copy operation by default in Windows. Using the Shift key, it becomes a move operation (but internally it’s a copy and a delete operation).
However, dragging and dropping files within the same volume defaults to a move operation (but internally it’s a filesystem operation only, the data stays where it is). As a result, dragging a 8 GiB file from C:\Foo\ and dropping it at C:\Waldo\ is a very fast operation. That’s because Windows doesn’t have to copy the actual data. But as soon as you press Ctrl before dropping the file it will do just that.
Depending on the access method, you can get closer or further away from physical disk drive. Internal computer drives are DAS devices. The WD My Cloud is a NAS device. The network presents a layer of abstraction, which makes the physical drive inside the NAS less transparent to the computer accessing it. The computer doesn’t quite see that the same way it does the internal drive. You would need a SAN device to make that more transparent to the computer. That way you may be able to do all kinds of operations on just like on an internal drive.
Generally, to speed up a cabled network connection you would want to use as short cables as possible, 1 Gigabit Ethernet NIC or better at each end, and at any point in between like switches and routers. Use proper, certified cables for the chosen network standard.