I've personally found a brand new, or at least very sharp, single edge razor blade to be very effective. You can buy a 100 pack of them for around $7 (US) at your local home store. Just slice the trace at both ends of the section you want to remove, then you can lift the removed copper right off with the corner of the blade.
I find they're better than an x-acto or utility knife as you get 200 fresh sharp edges that really slice through the copper cleanly with little force, so it minimizes the chance of slipping and cutting more than you bargained for.
Of course you do have to be careful with the blade, as they don't come with quite as nice of a handle...