How do I put new banana connector on with other wires showing up after cutting ?

Can you put details to your story?

That will be helpful.

On the other hand, you've already connected one banana, but I'm still trying to understand what's wrong with the other banana and how it's not same?

that naked wire isn't the right color.  but that banana plug is nothing to brag about either.  

bottom line is speaker wires are one conductor (per color).  no shield, no ground.  so perhaps a bastard wire was used to make the the cables and an extra conductor wasn't used.

If I needed new cables I'd buy bfa connectors and some woven audioquest knockoff wire on ebay for $10/foot and make yourself some much nicer cables for a hundred bucks or so depending on length.

Jerry

what wire is that? looks like an interconnect cable, not a speaker wire

what are you trying to do?

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I use these banana connectors for speaker wires, the 2 set screws give great hold, and the pin inside the banana pin tightens the banana pin when in the socket.

angled design allows 2nd cable to be ’patched’ in.

https://www.parts-express.com/Stacking-Banana-Plug-with-Dual-Set-Screws-Poly-Carbonate-Sh-091-3608?quantity=1