I broke the mast hitting a tree, so need to replace it. Once before the rope broke and so I also have an intact mast with a broken rope. There is a little of the broken rope still attached to the good mast.

Is there any way to detach the intact rope from the broken mast, and the broken rope from the intact mast, and use the good parts to effect a repair? Or are the only options to either purchase a new mast and rope or replace the entire antenna unit?

You'll need a whole new mast.