You cant save your whole database within tableau , you can connect to tables which are required and join them if need and create a extract instead of live connection.
If its live connection evry time when you open the dashbaord you need to provide credentials if it is extract your data will be stored in RAM and you can use it without DB.
Use extract connection in your scenario and whole database wont save in your Tableau whatever required tables you can save as extract.
Hope this helps
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Thank you, Naveen!