So I had a clogged drain and I was checking the trap. I was under the house and was working on the pipes when I accidentally broke the drain pipe off at a T joint just below the trap. How can I remove the broken end from the joint since it was solvent welded in? Or what else can I do?

There is a couple of things to do, one is to cut out the TEE out of the line and replace it using neoprene couplers that are approved for this sort of thing. But since you would have to do that if my idea does not work here is what I suggest. Cut the broken pipe off even with where it enters the TEE. Then use only a hack saw blade, wrap a cloth around one end to protect your hand, with the other end, cut the broken piece of PVC twice about 3/8th of an inch apart, make these cuts straight into the pipe the same way that the pipe is running. In other words if water was running through the pipe, cut the same way the water would run. Make these cuts just deep enough to go through the broken pipe, no further, in fact you do not have to go all the way down to the TEE, just almost to the Tee. Once you have the cuts made look at the end of the
Tee and the pipe, you can see where the two join together, With a very sharp bladed screwdriver put the tip right on the seam where the joint is and right in the middle of the two slots you cut into the pipe. Now tap the screwdriver lightly straight into the seam, try to follow the crack between the Tee and the PVC pipe that is left in the tee. The little slot that you cut out should pop out, as it does then move your screwdriver tip to one side of the gap you have made and repeat the tapping of the screwdriver, unless this is a perfect joint, you should be able to get the completer piece of pipe out and then you can put in a new piece of pipe and you can cut the other piece smooth and use a coupling to piece the two together.
One word of warning as you are tapping the screw driver into the crack do not try to pry the pieces out, just let the thickness of the screwdriver crack the glue joint and then move around another little bit and do it again.

Even if you ruin the tee you can still cut the tee out and go back with the joints I mentioned at first. Good Luck