A USB cable consists of a number of wires attached to connector plugs at both ends. A cut in the end of one of the connectors on the USB cable can cause a wire to break off, rending the USB cable useless. To be able to again use the USB cable, replace the connector and reconnect the wires yourself. A few tools common in most households will be needed, as will some experience in using a soldering iron.
Cut off the broken end of the USB cable with the blade of a utility knife. Dispose of the cut end in the trash.
Cut a 1-inch slit from the cut end of the USB cable. Pull the insulation away from the inner wiring with your fingers. Separate the wires that were inside the insulation from each other.
Strip a half-inch of insulation off the ends of all of the wires with the wire strippers.
Place a sheet of newspaper on a table to protect the surface. Place the USB connector on the newspaper with the contact slots at one end closest to you.
Solder the exposed ends of the wires to the contact slots on the USB connector in the following order: the red wire to the extreme right slot on the connector; the white wire to the slot on the connector next to the red wire; the green wire to the slot on the connector next to the white wire; the black wire to the slot on the connector's extreme left side.
Let the solder cool. Wrap the end of the connector with strips of electrical tape to cover the wiring connected to it.
Use as fine a tip as possible on the soldering iron.