When I turn the mouse on the green light blinks twice, pauses, then repeats and repeats. Batteries are new and my other mouse works fine.

It isn't pairing with Bluetooth. Go to System Preferences/Bluetooth and make sure it is turned on. If required, borrow a wired mouse.

Bluetooth devices become unresponsive

Bluetooth Interference Sources

Bluetooth Interference Sources (2)

If your Wi-Fi is capable of generating a 5 GHz signal, try that.

Alternatively, your batteries are not connecting properly.

Clean the contacts inside of the battery compartment and then the new batteries themselves (in case they have been contaminated.

What brand of batteries are you using. I ask because some batteries are slightly smaller than required because they are either fakes or of inferior manufacture.

I had a similar issue where the wireless mouse refused to connect to Bluetooth. If I got it to pair it tracked erratically as if it was dirty or the surface was not reflecting. Since BLE and WiFi are both 2.4GHz I decided to shutdown WiFi and the mouse began to work normally. I decided to switch to my Routers 5.0GHz band and now the mouse is working just fine. It is worth a try...