It is crucial to have focused mode when we are working. It is to enable deep work in a specific important task before we are distracted by the trivial stuff.
The trivial stuff; reading email is one of it. Therefore, it is good to disable all distraction and have an allocated time to respond to the email. Email responses can wait.
One of the simplest ways is to disable all notifications and alert to your email client. Here is the example to do it in Microsoft Outlook 365.
Disable all notification on Outlook Options
Go to File -> Option -> Mail and then disable all message arrival notification and click ok to save.