Nobody ever asks me this, but maybe there are some people who want to know. Here's how I cut thin lines.
1. Cut from left to right (unless you are left-handed, then cut from right to left).
2. Keep blade SHARP! Dull blades will rip paper more often than a slip of your hand will.
3. Practice! Practice! Practice!
I made a sheet with illustrations and everything about cutting thin lines. You can download a copy here in vector format: How to Cut Thin Lines