This seems to have been a problem for a L-O-N-G time now. Here is a issue from 2009: Copy and paste issues on google crome
While I am not a fan of Safari and I really hate FF, I found Chrome fast but full of issues. My fix? Opera.
It's not great, but it seems to be the best that we've got at present. I am using it exclusively across platforms - OS X, Linux and Windows 7 - and it is very stable.
It's based on the Chrome engine, but doesn't seem to have the issues Chrome has. For example, I have yet to deal with the Cut/Paste issue on OS X 10.10 and Opera.