Crank removal tool broke. Before I buy another, what did I do wrong? In my (first) attempt to remove the crank arms from a bike, I broke the crank puller (Super B TB-6485). I applied more force than I was comfortable with, thinking the threads had perhaps rusted over time. When attaching the puller to the crank, I pulled back the driver a fair bit from the coupler, screwed in the coupler, tightened it lightly with a spanner, and then proceeded to turn the driver down as far as I could. I then applied as much pressure as I could, and I heard it snap. Uncoupled everything, and the two bits seen in images 1-3 fell to the ground.

What did I do wrong here? Can the tool be used without the parts that fell out? Should I have removed them beforehand? I'm honestly a little confused as to their function.

Thanks in advance. Images below.
You shouldn't use the little adapter that you can disassemble from the tool for a square taper crank. Check, but you should find that it has a larger diameter than fits through the square hole in the cranks. It is used for Octalink, ISIS etc cranks with a larger spindle.

What I think happened is you got a little way with the tool, then the adapter bottomed out against the crank itself (not the spindle). You were then effectively trying to pull the tool apart against itself, and succeeded. 

You probably don't need to buy another. You should be able to use the disassembled puller to remove the crank, and the adapter should still work on suitable cranks, just not this crank or other square taper ones.