The second example follows an apparently grammatically correct pattern, in which a pronoun (“them”) substitutes for a noun (“the trees”) in a correct sentence “We shouldn’t cut down the trees”. However, in reality pronouns are never used in this position with phrasal verbs (at least, I can’t think of any examples), and the second sentence is actually wrong.
All sentences should start with a capital letter and finish with a full stop (or exclamation mark or question mark). Full stops should be followed by spaces. For example, your first pair of sentences should be written:
The trees provide oxygen. We shouldn’t cut them down.
To say “We shouldn’t cut down the trees.” is totally correct and I am sure about it because it has the actual noun “the trees” in it.
but as my knowledge tells me that it is wrong to say “We shouldn’t cut down them” because “them” is a pronoun that REFERS to the trees,and we should say “We shouldn’t cut them down”
I just want to know if my (so called)knowledge is GRAMMATICALLY correct!!
Later I thought of the counterexample “get over it” (meaning “recover from something”). “get it over” has a different meaning of “finish something unpleasant”.
Of course there are many cases like “sit through it”, “step over it”, “climb up it”, etc., but I would say these are more ordinary preposition uses than phrasal verbs.