Communication between DB servers outside Active Directory
Because the machines are on different domains, you cannot use Windows/Integrated authentication. For mirroring, you can use certificates instead. The place to start is here: 

https://docs.microsoft.com/en-us/sql/database-engine/database-mirroring/setting-up-database-mirroring-sql-server. 

In that article, there is a specific section that links to the details of setting up certificates for outbound and inbound traffic. 

https://docs.microsoft.com/en-us/sql/database-engine/database-mirroring/use-certificates-for-a-database-mirroring-endpoint-transact-sql.