Is a torn DV tape recoverable in any way?
Mini DV tapes can be spliced, so it should be easy enough to reattach it to the reel in similar way. Be sure to use tape splicing tape and not any other kind of tape. Be sure to only put splicing tape on the substrate of the video tape. Don't let the tape fold over onto the oxide side. If you end up splicing in the middle of the tape, you will see the picture pixelate and freeze around the splice.

I would recommend running the repaired tape through your player last just in case something isn't quite right with your splice and you accidentally damage the head.