My quill stem on a recently acquired bike was totally seized. I tried bashing, twisting soaking it in solutions. Rather hastily, I decided the easiest and quickest way to get it out was to cut it out, since the stem was destined for the junk bin anyways.

Now, I lopped off the top of the stem to pull the fork out and made vertical cuts into the stem tube, but that piece of stem is still stuck.

To make matters worse, I accidentally broke off the inch and a half of stem that was sticking out the steer tube while trying to bash it out, so it is more or less flush with the top of it now.

The wedge is loose and but trapped by the piece of stem. Any one have ideas?

you could try to tap it out from the bottom of the fork if you can hit the very small flat part of the stem. Or Drill baby drill.

Should have locked the fork in a vise or something and then twisted the stem.

so you cut the bolt in half too? wedge is still in there,
take the fork out of the bike.. go find another fork.

No, sorry the bolt is out and the wedge is in there, but it is free/loose.

The only issue is finding a new fork, as this is a sort of beater bike, with a threaded fork.

ID of the steerer tube is 7/8 Inch , you may find a machine shop
with a big enough drill bit, to drill out the aluminum.

3/4 " should remove enough metal to peel out whats left.
without altering the tube ID.

Chuck up the drill in a Lathe then clamp the fork in

and run it into the drill , ... or use a Drill Press.

Well, I got it out.

What I ended up doing is chipping it out in about six different pieces using a flathead screwdriver and a hammer. It was pretty brutal and archaic, but it did the trick after a whole afternoon of loud whacks coming from my garage to disturb the neighbours.

I managed to dent the very of the steerer tube by accident, but with the help of a hammer and a conveniently sized and shaped seat tube was able to round it out again, and chase the threads a bit. This was by far the most difficult ordeal I've dealt with fixing up bikes.