Hello Giorgio,
I understand that your DB is SQL Server.
If you install your SAP system according to High Available Installation you can easily switch DB from one node to another. With HA option you use MS Cluster.
In you scenario you are using mirroring for HA. When you are using mirroring you should have virtual DNs for your DB Host. Othervise you should change DB host parameter in profile parameters and then try to open SAP.
Regards,
Yuksel AKCINAR