I would contact the company that made that pipe cutter and see if they have larger cutting wheels. I'm sure that you wouldn't be the first person to run across the problem of the cutting wheel being too small in diameter to cut off a floor flange.

While I'm sure that toilet flange would work, all the plumbers around here like the Oatey Twist-N-Set floor flanges:

Oatey Twist-N-Set Closet Flange at Blain's Farm & Fleet

It's too bad you already cut into your piping because the Oatey flanges also come in 3 inch diameter so that you could have just cut off the existing flange and installed one of Oatey's Twist-N-Set floor flanges inside what's left of your existing floor flange.

They also offer a 4 inch flange which should fit inside your existing pipe once you get the existing flange off.

The way this system works is that the plastic flange has a tapered thread on it similar to oil drill pipe threads. The rubber ring also has an internal tapered thread. You push the toilet flange into the pipe at and angle so that the pipe holds the rubber ring stationary, and you rotate the flange. As you rotate the flange, the rubber ring screws up the flange threads and expands to tighten up against the ID of the toilet drain pipe. It's a really good system that works every time. Home Depot here in Canada sells these, but I don't know about the US.