As for cups, if you can somehow get it it break a little on the side with the bottom intact, you could use tile nippers to go around the bottom and take it off in one piece. Usually when I break a cup I am trying to cut it in half. have you tried just dropping it on the floor? LOL Thats what usually happens to me then.
Seriously, Im sure slow or someone will have excellent advice.

gc- I very seldom get a whole round bottom from a cup. Every once in a while but it is always by addident. I start my nip close to the handle on either side and hold the bottom in my left hand and nip. Sometimes the handle comes loose and the cup cracks above the foot. If your cup cuts in half and you still want the bottom, nip around the outside of the foot all the way around each half and then join like a mosaic piece. It will be pretty round and look great. The bottles I cut the bottoms out with my saw but I think Delphi has a bottle cutter. Effrim's Bottle cutter and you lay your bottle in it and score around it and then tap and it breaks right off. That is all I can help you with maybe someone else has a secret to share. Good luck.

To get a bottle or glass bottom what you will need is:
1:one glass cutter/scoring tool
2:one pan or extream hot water (can be boiling but I don't use it)
3:one pan or bowl of ice water with lots of ice
4:gloves Like garden gloves or oven mitts)
5:eye protection
USE EYE AND HAND PROTECTION
-DO THIS AT YOUR OWN RISK-

-The bottles must not have lids on while doing this-

-Take said bottle and score the bottom as low as you can go or want. (It might help to set up a jig of some sort if you want straight lines)

-Once you have scored the bottle where you want it place the pan of hot water until the whole bottle is as hot as the water(may take a min or so). Sometimes at this point if the bottle is scored right it will break off then (not always).

-Immediately place the hot bottle into the ice water and the expansion and contraction of the glass should in the different temps should break the bottom of the bottle off. (Beware in this type of setting you learn if the bottle has hair line cracks anywhere else)

-If the bottom does not pop off at this point some gentle tapping should help ease the bottom off.

-then grind the edge to you desired finish

Hope this helps and good luck!

Phantom.....Wow...Thank you so much for the great information. I have a few colored bottles just waiting to be done....guess what I will be doing this afternoon? I so appreciate everyone's sharing on this site. Makes it fun and collaborative!! Yahoo.

So, Gardencrone.... how did the bottle cutting go this afternoon?