Chosen Solution
My new puppy chewed through the Chromecast wire, and it was working at first because it was still slightly together and I used reg tape around it to hold it, but then it completely ripped apart when spouse unplugged from wall. So I am wondering if I should just buy a new one? Or in some way can I fix it and strip the wire and put it back together?.
I would suggest you to get / purchase a new cable. From I see it is just a micro usb cable.
you may be able to strip the wire, re connect it, seal it and use it. I would simply buy a new wire.