Yes!
Make sure the cut is clean so there isn’t a short between the inner wire and outer one. And do be aware that you can get a slight shock from the exposed end; if this is a problem you might want to put some tape or heatshrink or dip the end in glue etc. You can also solder a JST pigtail to the leftover piece if you want to light it up. As stated above, here’s a good instructable on the procedure.
