I am getting a factory take off carbine barrel for a 10 /22 it will be going on my charger build. I have several ways to cut (hacksaw sawzall ext) I will decide when it gets here. My question is how do I cut it square? The profile of the 10/22 is very tapered and I cannot for the life of me come up with a method to level and square the barrel.
One idea I have is to level it off of the camber portion where it enters the receiver by clamping that portion in a vice using the pipe jaws padded and taped off of course? Any help will be appreciated.

Take a small hose clamp (or even a ring), slide it down the barrel then tape it off at the line.

It sounds like you’re asking two different questions. Cutting the barrel square and leveling the barrel are two different things.
When I was a hacksmith I did a similar operation on a Mauser.

You can use vice pads for cylinders instead of the pipe clamp on the vice and that should be enough to hold it depending on your vice.

You can rough it in with a hack saw.

You can purchase a cutter from Pacific Tool and Gauge, Chuck it in a drill, use lots of fluid, clear chips, and square the muzzle. Then use a crown cutter and cut it to the angle you want.

I believe that removing the barrel and using a lathe would do the job right if accuracy is a concern.

I bought a dovetail cutting jig, but you can make one yourself

take a 2" piece of square tubing, drill and tap one corner for a 1/4-20 bolt.
Then remove the bolt and heat the square tubing red hot and dunk in oil, this will harden the metal

Attach to the barrel just below your ugly non square cut, file the barrel down until the file hits the hardened metal on the square tubing (you will here the file skate across the hard metal) this way you can get it perfectly square.

If you're close to Oly, I'll chuck it up in my G4003G for you. I made a few Charger barrels out of old 10/22 barrels just a few weeks ago.