Cut and paste does exist on your Mac—it’s just slightly hidden.

The copy function is the same:

• “Edit > Copy” from the Finder menu
• Keyboard shortcut: ⌘C (command–C)

Now, instead of the paste function, select “Move Item Here”

• “Edit > Move Item” Here from the Finder menu (while holding the option key)
• Keyboard shortcut: ⌥⌘V (option–command–V)

You can also click and drag the item, while holding the command key.

That’s it. The item will be moved to the new location, and the original will gone.