There are two ways to clear your cookies in the MirageID browser. Which one you need to use will depend on whether you have Cookie Sync enabled. See here to make that determination.
Cookie Sync Disabled
If you are not using Cookie Sync, then you can clear your cookies by clicking on the 3-dot menu -> Settings -> Privacy and then click "Clear browsing data":
Cookie Sync Enabled
If you are using Cookie Sync, then you will need to clear your cookies centrally. Follow these steps:
Navigate to https://account.mirageid.com in any web browser and go to the Identities tab on the left sidebar
Click on the gear icon in the top left of the card for the Identity whose cookies you want to clear
Click on the "Clear Cookies" Link, and click Save
Cookies will now be cleared for all users of that Identity.