The ability to filter out an entire column is a feature request as selecting all values from a column to be filtered will also filter the rows associated with the column values being filtered.
The following Tableau Desktop idea I believe captures the feature: https://community.tableau.com/ideas/3274 Voting for ideas helps demonstrate support for the feature to the product management team.
Another potential workaround would to have the tables recreated within the data source, or mirrored in the data source, with the columns removed as desired.
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If you don't want the columns in your datasource at all, just hide them in the Data Source window after you've created the join. This also means that if you create an extract the columns won't be in the extract at all.