Yes, that is the basic about impaled objects, it can be tricky to cut down objects to the small size, I have seen lot of dangerous bleeding because people moved impaled object too much while they trying to cut it, so you need to be extra careful.
Do not forget that that impaled object actually stops (by closing blood vessels) bleeding, so if you move it too much you actually further “damage wound”.

And also it is not rare to see in the movies how as a part of first aid objects (arrows, knifes…) are being removed immediately from the wound, which is completely wrong.

It may be removed (rarely) if it is directly putting victim in danger of losing life (for example of an impaled object in mouth- unable to breath)