Blowing through the straw forces the ends of the cut straw to vibrate rapidly, creating a standing wave which can be heard easily. If you cut the straw the standing wave is shortened... making the the pitch higher as you have more oscillations in a given length of air. Try using two straws, whereby you can slide one over the other as you blow which creates mini-trombone effect!
Be careful demonstrating this to younger children; advise them of the dangers of scissors near your eyes, nose and mouth.
