The procedure you used is correct. I just tried it using LO Version 5.0.4.2 for Windows and it worked fine. I suggest you uninstall the version you have and download a current stable version from the web.
UPDATE: 2016.0211
After your last response, I created a csv file with some numbers and opened it in LO Calc. I then opened a new Calc file and tried numerous combinations of copy and paste. I did not experience the effect you describe.
In my opinion, there are only two possible explanations for the problems you are experiencing: 1) a corrupt csv file; or 2) a corrupt LO install.
STEP 1:
Test to see if there is some trash or corruption in the csv file. Try creating a sample csv file and performing some copy and paste tests as I did. If your results are the same as mine, there is something wrong with your original csv file.
If STEP 1 does not point to a resolution, proceed to STEP 2.
STEP 2:
Once again, I recommend you uninstall your version of LibreOffice, go to the web, and download and install a stable version of the latest release.
Good luck.