It is impossible to cut the dollar bill. Roll up a borrowed dollar bill and insert into inside of the tube. Then, push a blade right through the tube. When you remove the bill from the tube, it is safe and sound - in one piece!
This magic effect requires no practice. All you do is roll up a bill, and push the blade through the tube. Of course, you can perform this with a borrowed bill, which will dramatically increase its impact on your audience.