Import errors importing CSV to SQL Server table
At the end of the import/export wizard you have the option to save your SSIS package (yes that's what the wizard uses behind the scenes).  Save your package to a file then open it in SQL Server Data Tools.  Go into the data flow and open the source.  In the "Error Output" tab you will see an option to ignore failure (for truncation specifically or errors in general).  Modify it for the columns you are worried about.

All that being said you are probably(99.999%) not seeing a truncation because the column is to big to fit in a varchar(max).  What is probably happening is that SSIS "thinks" your column is shorter than it is.  If you go into the connection manager for your CSV file you can modify the "width" of your input columns in the advanced tab.