I have the exact same problem.
I am unable to copy or cut from most native apps and Google apps without my my screen going black (the upper status bar is still visible) and the phone freezes for 30 seconds or so, then I'm prompted with "Unfortunately, Chrome has stopped" message (with options to Report or Ok).
This problem occurs in quite a few apps, including SMS, Gmail, Chrome Browser, etc.
If I'm in an app like Twitter, I am allowed to select and copy or cut text. But when I go to paste that text in any app it seems as if the text is not saved in the clipboard.
I also get the following message when attempting to cut, copy or paste in WhatsApp "This functionality is not supported on you device".
It seems as if the copy, cut and paste functions have been disabled.
I first noticed this problem in early to mid December 2012.