Finder has copy and paste for files, but no cut. The move is done at the paste end: copy the file with ⌘C, go to the destination, and press ⌥⌘V. The Edit menu shows it as "Move Item Here" when ⌥ is held. The original disappears, as with cut and paste.
Other ways to move:
- Drag the file. Within the same disk a drag moves; to another disk it copies. Hold ⌘ while dropping to force a move, ⌥ to force a copy.
- Drag onto a folder in the sidebar or onto the path bar at the bottom of the window.
- Right-click → Copy, then right-click in the destination with ⌥ held → Move Item Here.
One habit to unlearn before it costs you files: dropping a folder onto a folder with the same name replaces it, it does not merge. See why dragging a folder replaces instead of merging.