In the new editor you cut directly on the timeline: no separate cutting mode anymore. These are the key moves.
Trimming: shorten the start or end
Click the element on the timeline and drag its start or end. The element shortens or extends to the length you want.
Splitting: divide an element
Place the playhead where you want to split. Zoom into the timeline with the slider on the right to hit the exact spot.
In the bar above the timeline, click Split item (shortcut cmd+K) to split only the selected element, or Split scene (shortcut cmd+Shift+K) to split the whole scene with all its layers.
Afterwards you can move, trim or delete the parts individually. To remove a section from the middle, split twice and delete the piece in between.
Cut, copy, duplicate, delete
You find all actions in the bar above the timeline: Cut (scissors), copy, paste, Duplicate (shortcut cmd+D) and the trash icon to delete.
Adjusting speed
Select the video element and set the Playback rate on the left, for example 2x for a timelapse or 0.5x for slow motion.
Tips:
The undo arrow at the top left reverts any cut.
The space bar plays and pauses, so you can check your cut right away.