Was digging in the yard and broke the PVC pipe connected to a metal pipe inside the joint. The PVC and joint is 3/4 inch however the PVC is glued inside the metal and now I can't get the old PVC out of the metal joint to replace it. I don't have any tools to cut the metal pipe. Is there anything I can do?

You could try melting it out with a propane torch and a wire brush.

Try using a pvc compression union to go over the metal pipe.
You don't say what size the metal pipe is.
Or you could try removing the broken pvc with a nipple extractor. The kind used in irrigation should work on pvc.