I googled where this phrase is from and providing the context would have been helpful.
It's a quote from The Jerusalem Post.
Hamas’s ability to take control of Judea and Samaria exists despite claims [by Israeli security services] that they are able to ‘keep the weeds freshly cut.’
It means that Israel can curb Hamas's recruitment in the two areas mentioned.
Weeds is something undesirable.
Keeping weeds cut is something you do to stop them from spreading.
The phrase is figurative.
This is a potentially inflammatory topic; please don't comment on the political content.