If by “electrical wire” you mean home electrical wiring for a 120V or 240V system, then the safe, approved, electrical-code-conforming, and won’t-burn-your-house-down way of splicing an electrical wire is to install an electrical box (plastic is fine), put the two ends of the cut wire you want to splice into into the box, and put the cut end of the new wire into the box, and then tie the ends together with the correct wire nuts and the correct technique.
A bad splice can generate 15 amps of heat. If 15 amps are passing through, each Ohm of contact resistance (from corrosion, bad connection, or other) will produce 225 Watts of heat. It doesn’t take long to light a fire.
This is electrical installation 101. If you have any questions or concerns about wiring your home, you will need to contact an electrician.