Q: How do i shut down my mac without a mouse

You can use shortcuts to restart, sleep or turn off the Mac. Read > http://support.apple.com/kb/HT2448 To turn off the computer, hold Control, Option (Alt), Command and Eject keys

It is best to use the mouse if possible, but you can hold down the power button for a few sec. 

Hello:

Try resetting the PRAM and SMC (no mouse required).

Barry

I have this same problem, it just started this summer (2014) with my iMac, the mouse suddenly cuts out and does that blinking twice thing and refuses to reconnect unless you restart your computer and then it works like a charm. Did you ever find a solution to your mouse problem?