You have various ways to attack the problem:
1- cut a little of the cable near the mouse itself and ressolder it (solves the problem if the cable is broken). To check if the internal infrared leds are working, see them through a cell or digital camera (with the mouse cover open and connected to the power-on Amiga);
2- Mount one of the several hacks lying on Aminet and hook a PS/2 mouse in it;
3- Buy a Cocolino adapter (to the very same as option #2) from Elbox;
4- Hook a serial IBM/peecee mouse on the serial port of the Amiga and download the mouse software from Aminet (the worst solution: the mouse only works on Workbench).