when submit the Extension application?

According to the HSMP rule, the application for extension of visa should be submitted 1 month before expire date. However, it is said that the processing time for extension visa is now about 1.5~2 month.
So when should I submit my extension application? 1 month, 1.5 month, or 2 month?

Sorry submission date remains no earlier than 1 month to the expiry of the initial 12 month visa - it has nothing to do with processing times. If you send it earlier than this it will be returned to you.

I see. But what if my Visa is expired before the extension application was approved? Is it allowed to stay in UK without extended visa when original was expired?

You may legally remain in the UK until your extension application is decided by the HSMP Team/ Home Office. Make sure you submit your extension application before the expiry of your current HSMP visa to ensure your right of appeal is protected in case of a refusal - I am sure it won't come to this though and you will get a successful extension to 3 years unless you have been economically 'inactive' and/or absent from the UK for most of the 12 months.