Ok, so I have put up and taken off an Imperial ****load of wallpaper (that's = 1.25 U.S. ****loads).
Don't be scoring through the top surface and picking at it. You might as well try and build the Great Pyramid of Ghizeh by yourself, that will be easier than getting the paper off that way.
1st- just peel off the top surface, assuming it's probably a vinyl type wallcovering, then when the backing is exposed, apply a uniform coating of the Dif gel wallpaper stripper. This crap usually clogs the spray bottle and makes an unholy mess, I find it works more effectively after I spray it on the backing to distribute it evenly with a slightyly damp sponge. Wait a couple of minutes and then the backing should come off pretty easily...unless someone has used some type of badazz adhesive instead of the ordinary wallpaper paste. I just use a putty knife to get an edge loosened up and it usually can be peeled then without much effort.
The scoring tool thingy mostly doesn't work fer crap and is a last resort.