Scissors and blades
Although traditionalists might have a problem with using scissors and blades to help cut paper, it does have to happen sometimes. With that said, it rarely has to happen when you are doing the actual design of the origami piece.
Many of the origami patterns call for a square piece of paper, and unless you get commercial origami paper, you might have to cut your own to size. A good pair of scissors or an artist’s blade and a straight edge will do the trick.