Indeed you can, right down the line between the copper pads. Some strips even have a scissors symbol on them to indicate this purpose.
Additionally, if you clean up the copper again you can rejoin it by soldering connecting wires, so you can position modules of it around your case without buy another set. You won't get a volt drop until you starting getting around 5 metres of the stuff.
Edited to clarify - get yourself a fibreglass pencil for cleaning the copper pads/tracks, works a treat, just don't press your finger on the end of the pencil! Fibreglass and skin is bad.