I was experiencing this strange behavior with my Magic Mouse for some time now, and looking here and there on the Net showed many similar issues, with numerous software solutions, but, for me, none of them worked.
On my sluggish computer (MacBook Pro mid 2012) I had replaced my hard disk drive by a Fusion Drive disk, with the SSD at the place of the HDD, and a HDD drive in a HDD enclosure at the place of the optical drive. As far as I can remember, this is when the Magic Mouse problems started.
I noticed that this annoying behavior of my Magic Mouse occurred when there was intense HDD activity (i.e. Time Machine backups), as I could hear the HDD fiddling around, in the silent place where I live, and at the same time, the Magic Mouse going crazy (and even with Bluetooth disconnections).
Looking inside my MacBook, I then noticed how close from each other were the HDD in its enclosure, and the AirPort/Bluetooth board. Could this be the problem?
I then unmounted my Fusion Drive, removed the SSD and the HDD, positioned a new HDD in its original place, leaving the optical drive’s place empty. Time Machine backups are of course very useful…
Now, my Magic Mouse is normally responsive, and my MacBook Pro is sluggish again.
Planning to replace this HDD with a unique large SSD.