How can I improve my bread-scoring technique?
This is an annoying problem, you've gone through all the effort to make beautiful loaves and then the razor catches and makes an ugly mark, or even deflates the bread a bit.

This is most likely to happen on high hydration doughs as they tend to be stickier. The trick is to stop it from sticking in the first part of the cut. The best way to stop sticking is to oil the blade before each cut. I drop some on a paper towel and use that to apply it, some bakers use an oil sprayer. Water also works, you dip the blade in water before each cut. 

Also, there's technique. If you cut with the tip it's much more likely to catch, you need to cut with the flat of the blade. Don't press in hard, let the blade do the work.