You can turn on Send and Archive in your Gmail settings, and Mixmax will follow suit.
Open your Gmail settings by clicking the gear icon in the top right corner of Gmail and clicking See all settings.
Scroll until you see Send and Archive, and click to select Show “Send & Archive” button in reply:
Scroll down to the bottom of your settings page and click Save Changes.
If you are using the Mixmax compose window rather than the Gmail compose window, then you will be able to Archive replies by pressing Ctrl+Enter.
Check your Mixmax Composing settings to ensure this setting is enabled. Under Composing, scroll down to Message options:
Check the box next to Archive with Ctrl+Enter, and you will be able to use this command when you are composing a reply. You won't be able to use it when you're composing a new message because there is nothing to archive.