I have been using LibreOfice without difficulty…just updated to the latest version and now the cut and paste of text from web page does not work. I have cut and pasted from this same web page before without difficulty until I updated.
Oh yes, I see. I’ve cut the Google page, but it didn’t paste to LO; and now Google is down having no content 
You forgot to add version information for Libre and your OS, both of some importance.
I copy/pasted this page in a blank Writer document and it failed - that is to say, you don’t want to see how that looks, but the content made it.
Actually, there are more unclear with the question. What is the web browser? (They may have different issues depending on application and its version.) What is the page? (Some pages have their own copy protection.) Is the operation actually cut-and-paste? (It may make sense when text is taken from edit box, tut it will fail when read-only content is “cut”)… And yes, what does “not work” mean? Is text not pasted, or is result unsatisfactory (e.g. formatting lost)?
So question isn’t asked