I found a USB mouse in the garbage it the optical type when you wiggle on the wire where it goes into the mouse you can actually make it work this means the wire is broke at this point what I am wondering is how MANY wires are used from the outside the cable seems to have a seam down the middle indicating two wires hard part will be getting it hooked up correctly.The USB interface requires 4 wires. Three might also be a fifth wire as a shield.
Most often wire failure is in the area right next to the mouse, That is  the point if high stress.
Unless you like to work with small things, it is best to just replace the mouse.
Here is a video. (Skip the Ad.)
https://www.youtube.com/watch?v=krk74V9kOR0
Note that it takes him 10 min. to fix the cable.
Are you planning on rescuing this mouse ? ?

I have 3 older ones i can ship you...No charge...I cut the grommet on one side half way thru slide it back cut cable pulled enameled wires out TWISTED together soldiered cut 1" ELECTRICAL tape in half one piece on one side of wire  other piece on other side of wire cut grommet still fits tight enough to keep wire from sliding out put all the electrical taped ends in one place put cover on works great TIME 30 minutes.

[attachment DELETED by admin to conserve space]If it takes you 30 min.
And if the min. wage is $10.
You can pay yourself just  $5