clear up (v) vs. clear (v)

Solution 1:

I'm afraid that the definition for 'clear' you give doesn't exactly match your example sentences. We need the definition allowing 'place to be cleared' as DO, not the subsense with 'thing/s to be removed' as DO. CDE gives them both (bolding mine), though I feel the need to expand their definition in line with examples they give:

clear verb ... ​ B1 [ I or T ] to remove or get rid of whatever is blocking or filling something, or to stop being blocked or full [or to stop something being blocked or full]: ...

It took several hours to clear the road after the accident.

The definition for 'clear up' might perhaps also be misleading. M-W certainly offers

clear up British : to make an area clean or tidy

but Collins anticipates how precious it would be to speak of 'making tidy' a road surface covered in rocks:

'The highly complex operation will require protecting the road surface, bringing the rock down to the road level, breaking it up and removing it and then clearing up the road surface.' [Highland Council]

clear up 2. to put (a place or thing that is disordered) in order

..........................

So the two verbs (one simplex, one a MWV) mean different things. They may essentially converge in meaning, as clearing up a place may certainly involve removing some things completely:

The work crew soon cleared the road / cleared up the road.

However, when one clears a room say, he removes all removables completely:

I need you to clear your room by noon on Friday.

Whereas when one clears up one's room say, it may just be that everything that was strewn about the room is just tidied away onto shelves anfd into drawers etc:

You really must clear up your room, Toby.