To me, this seems like an unusual usage of phrasal verb get after :
get after 2.
To pursue something that is a problem or menace: If you don't get after those termites, your house will be destroyed.
(TFD) You get after [someone/something] (with something) .
Wareheim's usage strikes me as a (US) Southernism, and the article does state that the man has a home in North Carolina.
The usual construction would be Nothing you need to get after with a chainsaw yet.
(complete sentence) &rightarrow; [There is] nothing you need to get after with a chainsaw yet.
In other words, there is nothing yet that needs to be handled, cleared, or destroyed with a chainsaw.
ell.stackexchange.com/users/36187/Em.
So far [ yet , before some more severe destruction] there's nothing to go [get] after with a chain saw.
P. S.
Anyway, after points here at the source of trouble needing a chain saw to be applied.
Go after means 'to try to find' (e.g. to go after gold), to aim at something needing application of that instrument here.
As the other answer shows, the original get after expression has an even more direct meaning addressing something troublesome (with that instrument here).
ell.stackexchange.com/users/81024/Alex_ander
Another way of wording that sentence: So far there has been nothing that needed a chainsaw used on it before it could be removed.
After is being used in the sense of “applied to”.
ell.stackexchange.com/users/6361/jmoreno
We can get after something that needs tending or requires our action.
That is, we see that the thing gets done.
We tend to the matter.
I need to get after the backed-up laundry now that the washing machine has been repaired.
We can also get someone after something:
We need to get the dog-catcher after these packs of stray dogs.
And, in an extended, somewhat joking sense, we can get something after something:
I need to get the rake after those dead leaves.
That is, I need to rake those leaves.
The rake, being an inanimate object, cannot be given an assignment or a task to complete as the dog-catcher can.
And we can get after something with something.
You need to get after those tall weeds with a sickle.
A lawn mower won't do.
ell.stackexchange.com/users/10264/Tᴚoɯɐuo
I think it looks like an unusual usage of the word after .
It looks like it could simply be substituted with a for .
Nothing you need to get a chainsaw for yet.
In other words:After the winds as of yet, theres nothing you can't take care of without a chainsaw.
ell.stackexchange.com/users/82276/svin83
Wareheim said so far the wind has only knocked down branches and limbs small enough to be carried. "Nothing you need to get a chain saw  after  yet," he said by phone.   As I understand, the sentence is saying that:  Nothing you need to get a chain saw  after the hurricane is gone  yet .  But I'm not sure if my understanding is correct?  The  full source .
Help to understand the usage of "after" in "Nothing you need to get a chain saw after yet"
ell.stackexchange.com
<word-usage><sentence-meaning>
ell.stackexchange.com/questions/179818
ell.stackexchange.com/users/59517/dan
"Nothing you need to  get after  with a chainsaw  yet" would mean that there is nothing yet that needs to be handled, cleared, or destroyed with a chainsaw. This is an unusual usaage of the verb 'get after', which in this case means to apply to. You can get after a thing or person with something, so the sentence means that a chainsaw was not necessary to remove the small branches.
This is an unusual usaage of the verb 'get after', which in this case means to apply to. You can get after a thing or person with something, so the sentence means that a chainsaw was not necessary to remove the small branches.