It's always a good idea to place your stair
stringers on something like a set of sawhorses. Make a nice table by
placing some of your stair stringer material that hasn't been cut yet,
on top of two sawhorses.
This solves a couple of problems. It gives you a nice safe place to cut
the stair stringers and provides you with something to catch this scrap
triangular shaped pieces of wood, instead of them falling down, bouncing
off of the floor and hitting you in the legs.
Split Level Stair Framing