Why does the Magic Mouse prevent me from clicking with my trackpad?
This is a feature, not a bug. The idea is that you might want to disable the trackpad if you are using a mouse because, for example, you accidentally hit the trackpad with the palm of your hand.

I thought it was turned off by default, but in any case, here’s how to turn it on or off:



System Preferences » Accessibility » Mouse &amp; Trackpad 

[ ] Ignore built-in trackpad when mouse or wireless trackpad is present 

For more details: OSX Daily: Ignoring Built-in Trackpad Input When Using External Mouse with MacBook

Turning Bluetooth On / Off Without the Mouse

1) If you have brew installed, you can easily install blueutil via brew install blueutil. Then you can disable Bluetooth by going to Terminal and typing:

blueutil --power 0

2) “Full Keyboard Access” can also help:



Once that is enabled, open Bluetooth preferences in System Preferences and press Tab to highlight the “Turn Bluetooth Off” button, as shown here:



Then press the Spacebar to turn Bluetooth Off.

3) If you use Alfred or LaunchBar, I suspect they probably have tools to allow you to toggle bluetooth as well.