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

SPEAKER Cable may have solid or stranded wire, and there could be a ground wire or woven wire sheath for the cable included. Generally, when multiple wires are used they join somewhere behind the ends of the cable so you only see a twisted pair when you change the connector. You may have cut the cable back too far.  I suggest you go to Audioquest.com and look up the differences in how speaker cables are assembled. You may even discover the reason your particular cable has the wire it has.