When my son did his pots he knocked the bottom out by putting a socket in it and lifting the pot hard enough to get the socket to come up to his hand and then quickly pushing it down, giving the socket enough force to break out the bottom (a trick I used to use with a nail and glass soda bottle to break out the bottom to make a funnel). He did break a few pots in the process but finally got the desired result.
He, too, buried the rest in the substrate. He did try breaking them in half but didnt have any success. He has 4 whole pots (minus the bottoms) in his tank and I think he went through 8 others that were broken. He tried scoring the sides and tapping with a hammer - no luck. He tried a cold chisel with the pot on a 2X2 sitting inside - no luck. Both methods broke the pot every time. Rather than break more, he half-buried the ones with the bottoms knocked out into the substrate.
There may be a way, I dont know, short of using a ceramic saw. If you find out, please post it. We would be most interested.
Why do I love fish? Because every time I stare into the little world I have created for them, every problem I have just floats away....