My wireless Apple Mouse has stopped working.

A mouse could just fail, indeed at the end of its life it can do nothing else. I think your first test is to hold the mouse upside down and check if you have a green light showing. If so, the batteries are probably ok. if the light flickers it is quite likely the connections are at fault. Clean the inside of the battery compartment thoroughly in case there is any residue from previous batteries. Clean your battery connections and try again. You could also, try your mouse (indeed, both of them) with another computer, perhaps that of a friend. It doesn't matter if it is a pc. That will confirm the efficacy of the mice.

Magic Mouse 2 has been designed and developed for El Capitan (10.11.3) ... so older mice may not function quite so well but I haven't heard any complaints yet.