Will cutting sand paper with scissors make the scissors sharper or duller?

Duller

Scissors are sharpened by honing the narrow "chisel" edges, not the broad flat edges where the two blades sandwich together. Here's an image of someone sharpening tiny scissors with an even tinier file:

So, cutting sandpaper will abrade the point between the chisel edge and flat edge.

*You can use the sandpaper to re-sharpen the scissors afterwards, if it makes you feel better!

Sand paper removes material. When used properly, that removal of material can make a blade sharper. However, when cutting the sandpaper, there is no attempt to structure the removal of the material. It will simply dull the scissors. It will remove material in a relatively haphazard manner, taking off the sharp edge.

If you have any questions of this, ask someone who sews for their nice fabric scissors, and let them know you're going to go cut some paper with them. Find out how quickly they respond in an effort to avoid dulling their scissors. Perhaps its not the most scientific approach, but it is a well documented one, and very evidence based! And that's just normal paper!