Man, you're soo close!

1) Create your tumbler in polygons
2) Copy this tumbler and move it off to the side
3) Create a cube that encompasses the bottom of the glass
4) Select the glass, then the cube & do booleans->Difference
5) Select this block and do Polygons->Seperate
6) Delete the bottom chunk
7) Move the copy of the glass back to the origin

Simon.

In a picture: