update 2021 Better ice cutting pictures are on this post.
However, last week I gave a talk on ice at Portland Cocktail Week with Evan Zimmerman and Jim Romdall. During the talk one of them (Evan I think) mentioned how you use an ice pick to cut apart a block of ice the easy way.
I cringed thinking of all the time I'd spent sawing when this way is like 1000 times easier. I hope I can save you from the same fate.
1. Start with your slab of ice. The one in this picture is about 5 inches thick.
2. Tap a line across the top where you want the ice to break. The ice will chip off and form a little groove.
3. Tap in one point in the center. Poke hard. Poke poke poke.
4. The ice should break in two roughly along the line. Hooray!
5. Repeat the process to break it into smaller pieces.
An index of all of the ice experiments on Alcademics can be found here.